{"id":570,"date":"2020-01-26T15:09:07","date_gmt":"2020-01-26T15:09:07","guid":{"rendered":"http:\/\/localhost\/?post_type=knowledgebase&#038;p=570"},"modified":"2020-07-15T04:51:48","modified_gmt":"2020-07-15T04:51:48","slug":"practise-questions-functions","status":"publish","type":"knowledgebase","link":"https:\/\/ibalmaths.com\/index.php\/ibdp-math-hl-2\/functions\/practise-questions-functions\/","title":{"rendered":"Functions &#8211; Practice questions"},"content":{"rendered":"<p>Q1. Consider the function\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>f<\/mi><mfenced><mi>x<\/mi><\/mfenced><mo>=<\/mo><msqrt><mi>x<\/mi><mo>+<\/mo><mn>2<\/mn><\/msqrt><\/math>\r\n \u00a0and\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>g<\/mi><mfenced><mi>x<\/mi><\/mfenced><mo>=<\/mo><mi>a<\/mi><mi>x<\/mi><mo>+<\/mo><mi>b<\/mi><\/math>\r\n . Find\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>a<\/mi><\/math>\r\n \u00a0and\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>b<\/mi><\/math>\r\n , if\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>f<\/mi><mi>o<\/mi><mi>g<\/mi><mfenced><mn>1<\/mn><\/mfenced><mo>=<\/mo><mn>2<\/mn><\/math>\r\n \u00a0and\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>g<\/mi><mfenced><mrow><mo>&#8211;<\/mo><mn>1<\/mn><\/mrow><\/mfenced><mo>=<\/mo><mn>2<\/mn><\/math>\r\n \u00a0 \u00a0.<\/p>\r\n<div id=\"link1-link-570\" class=\"sh-link link1-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link1', 570, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link1-toggle-570\">Solution<\/span><\/a><\/div><div id=\"link1-content-570\" class=\"sh-content link1-content sh-hide\" style=\"display: none;\"><br \/>\r\nComing soon<br \/>\r\n<\/div>\r\n<p>Q2.If\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>f<\/mi><mfenced><mi>x<\/mi><\/mfenced><mo>=<\/mo><mi>sin<\/mi><mi>x<\/mi><\/math>\r\n \u00a0and\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>g<\/mi><mfenced><mi>x<\/mi><\/mfenced><mo>=<\/mo><msup><mi>x<\/mi><mn>3<\/mn><\/msup><\/math>\r\n then find the value of\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>g<\/mi><mi>&#959;<\/mi><mi>f<\/mi><mi>&#959;<\/mi><mfenced><mrow><mi>g<\/mi><mi>&#959;<\/mi><mi>g<\/mi><mo>+<\/mo><mi>g<\/mi><\/mrow><\/mfenced><\/math>\r\n .<\/p>\r\n<div id=\"link2-link-570\" class=\"sh-link link2-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link2', 570, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link2-toggle-570\">Solution<\/span><\/a><\/div><div id=\"link2-content-570\" class=\"sh-content link2-content sh-hide\" style=\"display: none;\"><br \/>\r\nComing soon<br \/>\r\n<\/div>\r\n<p>Q3. If\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>f<\/mi><mfenced><mi>x<\/mi><\/mfenced><mo>=<\/mo><mi>ln<\/mi><mfenced><mfrac><mrow><mi>x<\/mi><mo>&#8211;<\/mo><mn>1<\/mn><\/mrow><mrow><mi>x<\/mi><mo>+<\/mo><mn>1<\/mn><\/mrow><\/mfrac><\/mfenced><\/math>\r\n \u00a0and\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>g<\/mi><mfenced><mi>x<\/mi><\/mfenced><mo>=<\/mo><mfrac><mrow><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mn>2<\/mn><mi>x<\/mi><\/mrow><mrow><mn>2<\/mn><mi>x<\/mi><mo>+<\/mo><mn>1<\/mn><\/mrow><\/mfrac><\/math>\r\n then find the value of<\/p>\r\n<p>\r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>g<\/mi><mi>&#959;<\/mi><mi>f<\/mi><mfenced><mfrac><mrow><mi>e<\/mi><mo>+<\/mo><mn>1<\/mn><\/mrow><mrow><mi>e<\/mi><mo>&#8211;<\/mo><mn>1<\/mn><\/mrow><\/mfrac><\/mfenced><\/math>\r\n .<\/p>\r\n<div id=\"link3-link-570\" class=\"sh-link link3-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link3', 570, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link3-toggle-570\">Solution<\/span><\/a><\/div><div id=\"link3-content-570\" class=\"sh-content link3-content sh-hide\" style=\"display: none;\"><br \/>\r\nComing soon<br \/>\r\n<\/div>\r\n<p>Q4. Given\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>f<\/mi><mfenced><mi>x<\/mi><\/mfenced><mo>=<\/mo><mfrac><mrow><msup><mn>25<\/mn><mi>x<\/mi><\/msup><mo>&#8211;<\/mo><mn>1<\/mn><\/mrow><msup><mn>5<\/mn><mi>x<\/mi><\/msup><\/mfrac><\/math>\r\n \u00a0, check whether\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>f<\/mi><mfenced><mi>x<\/mi><\/mfenced><\/math>\r\n \u00a0is an odd function or an even function.<\/p>\r\n<div id=\"link4-link-570\" class=\"sh-link link4-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link4', 570, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link4-toggle-570\">Solution<\/span><\/a><\/div><div id=\"link4-content-570\" class=\"sh-content link4-content sh-hide\" style=\"display: none;\"><br \/>\r\nComing soon<br \/>\r\n<\/div>\r\n<p>Q5.\u00a0Check whether the function\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>f<\/mi><mfenced><mi>x<\/mi><\/mfenced><mo>=<\/mo><mfrac><mrow><mi>x<\/mi><mfenced><mrow><mn>1<\/mn><mo>&#8211;<\/mo><msup><mn>5<\/mn><mi>x<\/mi><\/msup><\/mrow><\/mfenced><\/mrow><mrow><mn>1<\/mn><mo>+<\/mo><msup><mn>5<\/mn><mi>x<\/mi><\/msup><\/mrow><\/mfrac><\/math>\r\n \u00a0is an odd function or an even function.<\/p>\r\n<div id=\"link5-link-570\" class=\"sh-link link5-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link5', 570, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link5-toggle-570\">Solution<\/span><\/a><\/div><div id=\"link5-content-570\" class=\"sh-content link5-content sh-hide\" style=\"display: none;\"><br \/>\r\nComing soon<br \/>\r\n<\/div>\r\n<p>Q6.\u00a0Find the value of\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>f<\/mi><mfenced><mfrac><mn>1<\/mn><mn>21<\/mn><\/mfrac><\/mfenced><mo>+<\/mo><mi>f<\/mi><mfenced><mfrac><mn>2<\/mn><mn>21<\/mn><\/mfrac><\/mfenced><mo>+<\/mo><mi>f<\/mi><mfenced><mfrac><mn>3<\/mn><mn>21<\/mn><\/mfrac><\/mfenced><mo>+<\/mo><mo>.<\/mo><mo>.<\/mo><mo>.<\/mo><mo>.<\/mo><mo>.<\/mo><mo>.<\/mo><mo>.<\/mo><mo>.<\/mo><mo>.<\/mo><mo>.<\/mo><mo>.<\/mo><mo>.<\/mo><mo>.<\/mo><mo>.<\/mo><mo>+<\/mo><mi>f<\/mi><mfenced><mfrac><mn>20<\/mn><mn>21<\/mn><\/mfrac><\/mfenced><\/math>\r\n \u00a0\u00a0 if\u00a0\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>f<\/mi><mfenced><mi>x<\/mi><\/mfenced><mo>=<\/mo><mfrac><msup><mn>9<\/mn><mi>x<\/mi><\/msup><mrow><msup><mn>9<\/mn><mi>x<\/mi><\/msup><mo>+<\/mo><mn>3<\/mn><\/mrow><\/mfrac><\/math>\r\n \u00a0.<\/p>\r\n<div id=\"link6-link-570\" class=\"sh-link link6-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link6', 570, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link6-toggle-570\">Solution<\/span><\/a><\/div><div id=\"link6-content-570\" class=\"sh-content link6-content sh-hide\" style=\"display: none;\"><br \/>\r\nComing soon<br \/>\r\n<\/div>\r\n<p>Q7.\u00a0Find the inverse of the function\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>y<\/mi><mo>=<\/mo><mfrac><mrow><msup><mi>e<\/mi><mi>x<\/mi><\/msup><mo>&#8211;<\/mo><msup><mi>e<\/mi><mrow><mo>&#8211;<\/mo><mi>x<\/mi><\/mrow><\/msup><\/mrow><mrow><msup><mi>e<\/mi><mi>x<\/mi><\/msup><mo>+<\/mo><msup><mi>e<\/mi><mrow><mo>&#8211;<\/mo><mi>x<\/mi><\/mrow><\/msup><\/mrow><\/mfrac><\/math>\r\n \u00a0.<\/p>\r\n<div id=\"link7-link-570\" class=\"sh-link link7-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link7', 570, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link7-toggle-570\">Solution<\/span><\/a><\/div><div id=\"link7-content-570\" class=\"sh-content link7-content sh-hide\" style=\"display: none;\"><br \/>\r\nComing soon<br \/>\r\n<\/div>\r\n<p>Q8.\u00a0Find the period of the function\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>y<\/mi><mo>=<\/mo><mi>sin<\/mi><mfenced><mfrac><mrow><mn>4<\/mn><mi>t<\/mi><mo>+<\/mo><mn>5<\/mn><\/mrow><mrow><mn>3<\/mn><mi mathvariant=\"normal\">&#960;<\/mi><\/mrow><\/mfrac><\/mfenced><\/math>\r\n \u00a0.<\/p>\r\n<div id=\"link8-link-570\" class=\"sh-link link8-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link8', 570, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link8-toggle-570\">Solution<\/span><\/a><\/div><div id=\"link8-content-570\" class=\"sh-content link8-content sh-hide\" style=\"display: none;\"><br \/>\r\nComing soon<br \/>\r\n<\/div>\r\n<p>Q9.\u00a0Find the domain of the function \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mn>3<\/mn><mi>x<\/mi><\/msup><mo>+<\/mo><msup><mn>3<\/mn><mi>y<\/mi><\/msup><mo>=<\/mo><mn>3<\/mn><\/math>\r\n .<\/p>\r\n<div id=\"link9-link-570\" class=\"sh-link link9-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link9', 570, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link9-toggle-570\">Solution<\/span><\/a><\/div><div id=\"link9-content-570\" class=\"sh-content link9-content sh-hide\" style=\"display: none;\"><br \/>\r\nComing soon<br \/>\r\n<\/div>\r\n<p>Q10.\u00a0Find the value of\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>a<\/mi><\/math>\r\n \u00a0for which\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>f<\/mi><mfenced><mi>x<\/mi><\/mfenced><mo>=<\/mo><mfrac><mrow><mi>a<\/mi><mi>x<\/mi><\/mrow><mrow><mi>x<\/mi><mo>+<\/mo><mn>1<\/mn><\/mrow><\/mfrac><\/math>\r\n \u00a0is\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>f<\/mi><mfenced><mrow><mi>f<\/mi><mfenced><mi>x<\/mi><\/mfenced><\/mrow><\/mfenced><mo>=<\/mo><mi>x<\/mi><\/math>\r\n \u00a0.<\/p>\r\n<div id=\"link10-link-570\" class=\"sh-link link10-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link10', 570, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link10-toggle-570\">Solution<\/span><\/a><\/div><div id=\"link10-content-570\" class=\"sh-content link10-content sh-hide\" style=\"display: none;\"><br \/>\r\nComing soon<br \/>\r\n<\/div>\r\n<p>Q11.\u00a0The graph of\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>f<\/mi><mfenced><mi>x<\/mi><\/mfenced><\/math>\r\n \u00a0is shown below in the domain\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>[<\/mo><mn>0<\/mn><mo>,<\/mo><mo>&#160;<\/mo><mn>4<\/mn><mo>]<\/mo><\/math>\r\n \u00a0and range\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>[<\/mo><mn>0<\/mn><mo>,<\/mo><mo>&#160;<\/mo><mn>2<\/mn><mo>]<\/mo><\/math>\r\n \u00a0. Sketch the graph of\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>&#8211;<\/mo><mi>f<\/mi><mfenced><mrow><mi>x<\/mi><mo>+<\/mo><mn>2<\/mn><\/mrow><\/mfenced><mo>+<\/mo><mn>2<\/mn><\/math>\r\n \u00a0.<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-980\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/01\/11.jpg\" alt=\"\" width=\"178\" height=\"203\" \/><\/p>\r\n<div id=\"link11-link-570\" class=\"sh-link link11-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link11', 570, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link11-toggle-570\">Solution<\/span><\/a><\/div><div id=\"link11-content-570\" class=\"sh-content link11-content sh-hide\" style=\"display: none;\"><br \/>\r\nComing soon<br \/>\r\n<\/div>\r\n<p>Q12.<\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-2126\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/01\/1..jpg\" alt=\"\" width=\"1105\" height=\"1031\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/01\/1..jpg 1105w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/01\/1.-300x280.jpg 300w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/01\/1.-1024x955.jpg 1024w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/01\/1.-768x717.jpg 768w\" sizes=\"auto, (max-width: 1105px) 100vw, 1105px\" \/><\/p>\r\n<div id=\"link12-link-570\" class=\"sh-link link12-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link12', 570, 'Solution12', 'Hide Solution12'); return false;\" aria-expanded=\"false\"><span id=\"link12-toggle-570\">Solution12<\/span><\/a><\/div><div id=\"link12-content-570\" class=\"sh-content link12-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-2127\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/01\/1.-1.jpg\" alt=\"\" width=\"685\" height=\"1209\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/01\/1.-1.jpg 685w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/01\/1.-1-170x300.jpg 170w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/01\/1.-1-580x1024.jpg 580w\" sizes=\"auto, (max-width: 685px) 100vw, 685px\" \/><\/p>\r\n<p>\u00a0<\/div><!-- AddThis Advanced Settings generic via filter on the_content --><!-- AddThis Share Buttons generic via filter on the_content -->","protected":false},"excerpt":{"rendered":"Q1. Consider the function\u00a0 fx=x+2 \u00a0and\u00a0 gx=ax+b . Find\u00a0 a \u00a0and\u00a0 b , if\u00a0 fog1=2 \u00a0and\u00a0 g&#8211;1=2 \u00a0 \u00a0. Q2.If\u00a0 fx=sinx \u00a0and\u00a0 gx=x3 then find the value of\u00a0 g&#959;f&#959;g&#959;g+g . Q3. If\u00a0 fx=lnx&#8211;1x+1 \u00a0and\u00a0 gx=x2+2x2x+1 then find the value of g&#959;fe+1e&#8211;1 . Q4. Given\u00a0 fx=25x&#8211;15x \u00a0, check whether\u00a0 fx \u00a0is an odd function or an [&hellip;]<!-- AddThis Advanced Settings generic via filter on get_the_excerpt --><!-- AddThis Share Buttons generic via filter on get_the_excerpt -->","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-570","knowledgebase","type-knowledgebase","status-publish","hentry","knowledgebase_cat-functions","no-wpautop"],"_links":{"self":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/570","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase"}],"about":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/types\/knowledgebase"}],"author":[{"embeddable":true,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/comments?post=570"}],"version-history":[{"count":17,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/570\/revisions"}],"predecessor-version":[{"id":2128,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/570\/revisions\/2128"}],"wp:attachment":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/media?parent=570"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}