[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-207728-en":3,"doc-seo-207728-105":30,"detail-sidebar-cat-0-en-105":90},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},207728,1099514068035,"Ezra","https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c",4,"Exam","FUNCTIONS - GCSE (+ IGCSE) Exam Question Practice","A set of GCSE (plus IGCSE) functions exam practice questions focusing on evaluating functions, combining them through multiplication/composition, and working with inverse functions. Tasks include substituting given values, solving for unknown parameters from function equations, expressing inverse functions in an explicit algebraic form, and identifying domain restrictions and excluded values. Further questions build gf and fg expressions and require simplified answers with clear working. Timed practice supports exam-style assessment.","FUNCTIONS  \n[ESTIMATED TIME: 75 minutes]  \nGCSE  \n(+ IGCSE) EXAM QUESTION PRACTICE  \n\n| 1. | [8 marks] |\n| --- | --- |\n| The functions f and g are defined as |  |\n| f(x) = 12 x + 4 |  |\n| g(x) = x~~ ~~1 |  |\n| (a) Work out f(6) |  |\n| (b) Work out fg(–3) | .........................................\u003Cbr>(1) |\n| (c) g(a) = –2 | .........................................\u003Cbr>(2) |\n| Work out the value of a. |  |\n| (d) Express the inverse function f–1 in the form f–1(x) = … | a = .........................................\u003Cbr>(2)\u003Cbr>f –1 ( x ) = ......................................... |\n\nContains questions which have been reproduced with the kind permission of Pearson Education Limited UK  \nQuestions compiled by:  \n@Maths4Everyone  \n(3)  \n2. [8 marks]  \n\"\\#1 L'.*,$-.% L +.3 8 +21 31L$.13 +% L-))-4%9  \nLM!N $ !~~ ~~J\"~~ ~~;  \n8M!N $ ! \\#J  \nM+N M$N \\,+,1 4\\#$*\\# V+)'1-L! *+..-,(1 $.*)'313 $. ,\\#1 3-/+$. -L L9  \n999999999999999999999999999  \nM$$N \\,+,1 4\\#$*\\# K,\u003C>70-L! *+..-,(1 $.*)'313 $. ,\\#1 3-/+$. -L 89  \n999999999999999999999999999  \nHPJ  \nM(N W+)*')+,1 L8MJ\u003CN  \n999999999999999999999999999  \nHPJ  \nM*N 56&21%%,\\#1 $.V12%1 L'.*,$-. 8RJ $. ,\\#1 L-2/ 8RJM!N ^ 999999  \n99999999999999999999999999999999999999999999999999999999  \n3. [6 marks]  \nf: x ! 2x–1  \n3  \ng: x ! , x ( 0 x  \n(a) Find the value of  \n(i) f(3),  \n(ii) fg(6) .  \n(2)  \n(b) Express the inverse function f–1 in the form f–1: x ! ...  \n...............................  \n(2)  \n(c) (i) Express the composite function gf in the form gf: x ! ...  \n...............................  \n(ii) Which value of x must be excluded from the domain of gf?  \nx =    \n(2)  \n4. [7 marks]  \n7KH IXQFWLRQ I LV GHILQHG DV  \n􀀂􀀇[􀀈 􀀂 [~~ ~~~~ ~~􀀊  \n􀀋D􀀌 )LQG I 􀀋􀀛􀀌  \n(((((((((((((((((((((((((((((((  \n􀀋􀀔􀀌  \n􀀋E􀀌 ([SUHVV WKH LQYHUVH IXQFWLRQ I ±􀀔 LQ WKH IRUP I ±􀀔 􀀋[􀀌 􀀑􀀑􀀑  \nI ±􀀔 􀀋[􀀌 ((((((((((((((((((((((((((((((((((((((((((((((  \n􀀋􀀕􀀌  \n7KH IXQFWLRQ J LV GHILQHG DV  \n􀀅􀀇[􀀈 􀀂 [ 􀀄 􀀄  \n􀀋F􀀌 :KLFK YDOXHV RI [ FDQQRW EH LQFOXGHG LQ D GRPDLQ RI J\"  \n((((((((((((((((((((((((((((((((((((((((((((((  \n􀀋􀀕􀀌  \n􀀋G􀀌 ([SUHVV WKH IXQFWLRQ JI LQ WKH IRUP JI 􀀋 [􀀌 􀀑􀀑􀀑  \n*LYH \\RXU DQVZHU DV VLPSO\\ DV SRVVLEOH􀀑  \nJI􀀋[􀀌 ((((((((((((((((((((((((((((((((((((((((((((((  \n􀀋􀀕􀀌  \n5. [7 marks]  \n\"\\#1 L'.*,$-. L $% 31L$.13 +% LM$N ^ $~~ ~~$'~~ ~~C 9 M+N c$.3 ,\\#1 Q+)'1-L  \nM$N LMKNT  \n99999999999999999999999999  \nM$$N LMRKN9  \n99999999999999999999999999  \nDEF  \nM(N Z,+,1 4\\#$*\\# Q+)'1M%N-L $ /'%,(1 16*)'313 L2-/ ,\\#1 3-/+$. -L L9  \n99999999999999999999999999  \nDPF  \nM*N M$N c$.3 LLM$N9  \nd$Q1 0-'2 +.%412 $. $,% /-%,%$/&)1 L-2/9  \nLLM$N ^ 9999999999999999999999999999999  \nM$$N E\\#+, 3-1% 0-'2 +.%412 ,-M*NM$N %\\#-4 +(-',,\\#1 L'.*,$-. Lj 99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999  \n99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999  \nD!F  \n6. [6 marks]  \nf(x) = x~~ ~~1  \n(a) Find the value of f(11)  \n........................................................  \n(1)  \n(b) State which value of x must be excluded from any domain of f  \n........................................................  \n(1)  \n(c) Find f􀀽1 (x)  \n........................................................  \n(3)  \n(d) State the value which cannot be in any range of f  \n........................................................  \n(1)  \n7. [7 marks]  \nf is the function such that  \nf(x) = 3xx+~~ ~~1  \n(a) Find f (0.5)  \n.......................................................  \n(1)  \n(b) Find ff(–1)  \n.......................................................  \n(2)  \n(c) Find the value of x that cannot be included in any domain of f  \n.......................................................  \n(1)  \n(d) Express the inverse function f–1 in the form f–1(x) = ...  \nShow clear algebraic working.  \nf–1(x) = .......................................................  \n8. [9 marks]  \n?6%7 _ 6% H D7F 6\\#7 C%&2 ?6[7  \n;;;;;;;;;;;;;;;;;;;;;;;;;;;;","cbCaivs8AnI9d0hF","https://ap.wps.com/l/cbCaivs8AnI9d0hF","pdf",927443,1,12,"English","en",105,"# Functions questions\n## Evaluate and combine functions\n## Inverse functions\n## Domain and range restrictions","[{\"question\":\"How are function values evaluated in these questions?\",\"answer\":\"The questions substitute specific inputs into the given function rules, such as calculating f(6) or f(1). Answers are then filled into the provided lines.\"},{\"question\":\"What does it mean to express the inverse function in the required form?\",\"answer\":\"The inverse must be rewritten algebraically as f–1(x)=… or f–1: x ! ... according to the question’s specified format. This typically involves solving the original function equation for x in terms of the output.\"},{\"question\":\"How do the questions test understanding of domain restrictions?\",\"answer\":\"They ask which x-values must be excluded from the domain (for example, where a function would be undefined). The required excluded value must be identified based on the function’s structure.\"}]","FUNCTIONS - GCSE (+ IGCSE) Exam Question Practice | PDF",1788600828,30,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":85,"head_meta":87,"extra_data":89,"updated_unix":28},"functions-gcse-igcse-exam-question-practice","",{"@graph":36,"@context":84},[37,53,67],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/exam/",3,{"item":52,"name":13,"@type":43,"position":11},"https://docshare.wps.com/document/functions-gcse-igcse-exam-question-practice/207728/",{"url":52,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":61,"encodingFormat":60,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-09-05",true,{"@type":64,"interactionType":65,"userInteractionCount":4},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80],{"name":71,"@type":72,"acceptedAnswer":73},"How are function values evaluated in these questions?","Question",{"text":74,"@type":75},"The questions substitute specific inputs into the given function rules, such as calculating f(6) or f(1). Answers are then filled into the provided lines.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"What does it mean to express the inverse function in the required form?",{"text":79,"@type":75},"The inverse must be rewritten algebraically as f–1(x)=… or f–1: x ! ... according to the question’s specified format. This typically involves solving the original function equation for x in terms of the output.",{"name":81,"@type":72,"acceptedAnswer":82},"How do the questions test understanding of domain restrictions?",{"text":83,"@type":75},"They ask which x-values must be excluded from the domain (for example, where a function would be undefined). The required excluded value must be identified based on the function’s structure.","https://schema.org",{"og:url":52,"og:type":86,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":88,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":91},[92,96,100,103,108,113,118,122,127,130,134],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":93,"show_sort_weight":94,"slug":95},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":97,"show_sort_weight":98,"slug":99},"Literature",80,"literature",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":101,"slug":102},70,"exam",{"id":104,"doc_module":4,"doc_module_name":46,"category_name":105,"show_sort_weight":106,"slug":107},5,"Comic",60,"comic",{"id":109,"doc_module":4,"doc_module_name":46,"category_name":110,"show_sort_weight":111,"slug":112},6,"Technology",50,"technology",{"id":114,"doc_module":4,"doc_module_name":46,"category_name":115,"show_sort_weight":116,"slug":117},7,"Healthcare",40,"healthcare",{"id":119,"doc_module":4,"doc_module_name":46,"category_name":120,"show_sort_weight":29,"slug":121},8,"Research & Report","research-report",{"id":123,"doc_module":4,"doc_module_name":46,"category_name":124,"show_sort_weight":125,"slug":126},9,"Religion & Spirituality",20,"religion-spirituality",{"id":125,"doc_module":4,"doc_module_name":46,"category_name":128,"show_sort_weight":125,"slug":129},"World Cup","world-cup",{"id":131,"doc_module":4,"doc_module_name":46,"category_name":132,"show_sort_weight":131,"slug":133},10,"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":46,"category_name":136,"show_sort_weight":104,"slug":137},19,"General","general"]