Day+2+-+WS+Topic+2.8+Inverse+Functions (1)
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MATHEMATIC 123
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Mathematics
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Dec 17, 2024
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2
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Worksheet A: Topic 2.8Inverse Functions Created by Bryan Passwater Worksheet A: (Topic 2.8) Inverse Functions Name:Directions: Find the inverse relation for the relation below. 1. Original Function Inverse FunctionDirections: For the given functions below, sketch the inverse function on the same axes as the original function. 2. 3. Directions: Find the inverses of the following functions. Write your answer with proper notation. Write the domain and range of each original function and its inverse.4. ?(π₯) =π₯ β 3π₯ + 26. π(π₯) =βπ₯ + 23β 57. β(π₯) =4π₯ β 12π₯ + 38. π(π₯) = βπ₯ β 4D: R: D: R: D: R: D: R: Find the inverse: Find the inverse:Find the inverse:Find the inverse:D: R: D: R:D: R:D: R:9. Show that?(π₯)and?(π₯)below are inverses. ?(π₯) = π₯2β 3, where π₯ β₯ 0 ?(π₯) = βπ₯ + 3, whereπ₯ β₯ β3. 10. Show thatβ(π₯)andπ(π₯)below are inverses where π₯ β 0 and π₯ β β2. β(π₯) =4π₯ + 2π(π₯) =4π₯β 2π₯β30?7?(π₯)12850π₯?β1(π₯)Using the original function table given, what is the value of ?β1(5) =_______
AP Precalculus βMixed Six βTopics 2.7 & 2.8 No Calculator Composition of Functions and Inverse Functions 1. Factual Recall 2. Carry out a Procedure 3. Classify a Mathematical Object Given ( )31fxx=+and ( )21.g xx=βa) Evaluate ( )()3.fgb) Evaluate ( )()3.gfc) The function fis invertible. Find its inverse()1.fxβxβ2 β1 0 1 2 ()fx0 2 3 0 β4 ( )g xβ4 β2 0 2 3 The table above gives values of the functions fand gat selected values of x. a) Evaluate ( )()1.fgb) Evaluate ()()1.gfβc) Find ( )12 .gβWhich one doesnβt belong?(Hint: Which one requires a restricted domain in order to be invertible?) ()21fxx=+()15g xx=+( )21h xx=+( )31j xx=+For the function you identified, give an example of a restricted domain that would make it invertible. 4. Prove, Show, Justify 5. Extend a Concept 6. Critique a Fallacy The graph of the piecewise function gis shown to the left. Let hbe the inverse function of g. Find the maximum value of h. Sketch the graph of hto verify your answer. x0 1 3 4 6 ( )k xβ4 β2 0 2 3 The table above gives values of the function k at selected values of x. The function jis given by ( )21.xj x=βa) Evaluate ( )()2.kjb) Evaluate ( )()1.j kSonia attempts to decompose the function hgiven by ()()()224415.9xxh xfg xxβ+==+She states that ( )2153xfxxβ=+and ( )2.g xx=What is wrong with Soniaβs decomposition? Find the correct functions for fand g. By Vicki Carter, Florence, SC