Gr 12 Maths – FunctionsCopyright©The Answer1GR 12 MATHSFFUUNNCCTTIIOONNSSQUESTIONS and ANSWERSWork through the Grade 11 Functions downloads first to ensureyour foundation is solid before attempting inverse Functions.We wish you the best of luck for your exams.FromThe Answer Series team

Gr 12 Maths – Functions:QuestionsCopyright©The Answer21.The graph offis . . .1.1 If the inverse offis the reflection offin the line y =then the graph of the inverse is:A.B.C.D.(2)1.2 Consider the graph offgiven above.1.2.1Write down the equation of the given function and ofthe inverse function in the formy = . . .(2)1.2.2 Hence complete:(a)f(x) = . . .(b)f-1(x) = . . .1.2.3Show how the equation off-1could have beencalculated from the equation off.(2)1.2.4 Explain whyfandf-1are both one-to-onerelations.(2)Sketch the graphs offandf-1on the same set of axes,indicating also the liney =x.3.3Write down the equation off-1in the formf-1(x) =. . . .3.4Arefandf-1both functions?Why (not)?4.Given:g(x) = 3x- 2.Determine each of the following:4.1g-1(x)4.2xg1( )4.3g1x⎛⎞⎝⎠(6)5.1Sketch the graphy = 2x,indicating the coordinates ofany three points on the graph.(3)5.2Use the three points on the sketch to write down thecoordinates of three points on the inverse function ofy = 2x.(3)5.3On the same system of axes, sketch the inverse functionofy = 2xand the liney =x.5.4Describe the transformation from the graphy = 2xto itsinverse in words and give the rule for this transformation.(2)5.5Write down the equation of the inverse function in theformx= . . .[In Topic 4, you will convert this equation toy = . . . ](2)5.6Are both the above graphs functions? Why (not)?(2)5.7Write down the domain and the range of the graphs of:(a)y = 2x(b)x= 2y(4)6.Consider the functionfwheref(x) = 26.1Write down the domain and range off.6.2Sketch the graph offandgon the same set of axeswheregis the reflection offin the line y =x,(2)2.Consider the functionf(x) = -3x+ 6.2.1Write down the domain and range off.(2)2.2Determine the equation of the inverse offin the formf-1(x) = . . .(2)2.3Sketch the graphs of the functionsf,f-1andy =the same set of axes. What do you notice?(3)xon2.4Iff(1) = 3, thenf-1(3) = . . . ?2.5f(2) = 0(;)lies onfand(;)lies on3.1Write down the coordinates of thex- and y-intercepts of thefunctionf(x) = 2x+ 6and off-1, the inverse function off(1)f-1. (2). (4)3.2Sketch the graphs offandf-1on the same set of axes,indicating also the liney =x.3.3Write down the equation off-1in the formf-1(x) =. . . .3.4Arefandf-1both functions?Why (not)?4.Given:g(x) = 3x- 2.Determine each of the following:4.1g-1(x)4.2xg1( )4.3g1x⎛⎞⎝⎠(6)5.1Sketch the graphy = 2x,indicating the coordinates ofany three points on the graph.(3)5.2Use the three points on the sketch to write down thecoordinates of three points on the inverse function ofy = 2x.(3)5.3On the same system of axes, sketch the inverse functionofy = 2xand the liney =x.5.4Describe the transformation from the graphy = 2xto itsinverse in words and give the rule for this transformation.(2)5.5Write down the equation of the inverse function in theformx= . . .[In Topic 4, you will convert this equation toy = . . . ](2)5.6Are both the above graphs functions? Why (not)?(2)5.7Write down the domain and the range of the graphs of:(a)y = 2x(b)x= 2y(4)6.Consider the functionfwheref(x) = 26.1Write down the domain and range off.6.2Sketch the graph offandgon the same set of axeswheregis the reflection offin the line y =(4)(2)(2)⎜⎟(3)x2(2)x.

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