University:
Missouri State University
Course:
MTH 136 | Precalculus 1
Academic year:

2019
Views:

228

Pages:

2
Author:

otrhjko

Pre-Calculus/Trig 3 UNIT 1: Algebra II Review – SECTION 6 WORKSHEET Name: _________________________ Date: _________________________ INVERSE FUNCTIONS Directions: Match the graph of the function with the graph of its inverse function. Inverse graphs are labeled A, B, C & D. 1.) 𝑓(𝑥) = C 𝑔(𝑥) = B 2.) 3.) ℎ(𝑥) = D Directions: Show that 𝑓 and 𝑔 are inverse functions both algebraically and graphically. 5.) 𝑓(𝑥) = 3 − 4𝑥 𝑔(𝑥) = 3−𝑥 4 3−𝑥 3−𝑥 𝑓(𝑔(𝑥)) = 𝑓 ( ) = 3 − 4( ) = 3 − (3 − 𝑥) = 3 − 3 + 𝑥 = 𝑥 4 4 𝑔(𝑓(𝑥)) = 𝑔(3 − 4𝑥) = 6.) 𝑓(𝑥) = 𝑥 3 − 1 3 3 − (3 − 4𝑥) 3 − 3 + 4𝑥 4𝑥 = = =𝑥 4 4 4 3 𝑔(𝑥) = √𝑥 + 1 3 3 𝑓(𝑔(𝑥)) = 𝑓(√𝑥 + 1) = (√𝑥 + 1) − 1 = 𝑥 + 1 − 1 = 𝑥 3 3 𝑔(𝑓(𝑥)) = 𝑔(𝑥 3 − 1) = √(𝑥 3 − 1) + 1 = √𝑥 3 = 𝑥 4.) 𝑗(𝑥) = A Directions: Determine whether the function has an inverse function. If it does, find the inverse function. 7.) 𝑓(𝑥) = 2𝑥 − 3 𝑓 −1 (𝑥) = 𝑥+3 2 3𝑥+4 5 5𝑥−4 3 OR 1 3 𝑓 −1 (𝑥) = 2 𝑥 + 2 𝑓(𝑥) = √4 − 𝑥 2 𝑓 −1 (𝑥) = ±√4 − 𝑥 2 11.) 𝑓(𝑥) = 𝑓 −1 (𝑥) = OR 9.) 8.) 1 𝑓(𝑥) = 2 𝑥 3 + 4 3 𝑓 −1 (𝑥) = √2𝑥 − 8 5 4 𝑓 −1 (𝑥) = 3 𝑥 − 3 10.) 1 𝑓(𝑥) = 𝑥 2 𝑓 −1 (𝑥) = 12.) 1 3 √𝑥 1 𝑓(𝑥) = 8 (𝑥 + 2)2 − 1 𝑓 −1 (𝑥) = −2 ± √8(𝑥 + 1) OR 𝑓 −1 (𝑥) = −2 ± 2√2(𝑥 + 1) 13.) 𝑥+1 𝑓(𝑥) = 𝑥−2 𝑓 −1 (𝑥) = −2𝑥−3 𝑥−1 OR 14.) 6𝑥+4 𝑓(𝑥) = 4𝑥+5 𝑓 −1 (𝑥) = −5𝑥+4 4𝑥−6 OR 2𝑥+3 𝑓 −1 (𝑥) = −𝑥+1 5𝑥−4 𝑓 −1 (𝑥) = −4𝑥+6