5. (3 pts) Find a formula for the inverse function ƒ¯¹(x) if f(x)=- Solution 1 Write y=- where x = dom(f). 2x+3 4x-1 Step 1: Solve for x in terms of y: 2x+3 4x-1 2x+3 y= 4x-1 >> 4xy-y=2x+3 4xy-2x-3+y (0, 1, 2) 2x(2y-1)=3+y ⇒ x=- 3+y 2(2y-1) with (y #1/2). Step 2: Interchange x and y: y 3+x 2(2x-1) with x=1/2 Therefore, the formula for the inverse function of f is given by: f(x)= (0, 0.5,1) 3+x 2(2x-1) Solution 2 Write y=- where x = dom(f). 2x+3 4x-1 Step 1: Interchange x and y: x=. 2y+3 4y-1 with (y =1/4)" Step 2: Solve for y in terms of x: 2y+3 x=- 4y-1 4xy-x-2y+3 ⇒ 4xy-2y=3+x (0,1,2) 2y(2x-1)=3+xy= 3+x 2(2x-1) with (x=1/2). (0, 0.5,1) Therefore, the formula for the inverse function of ƒ is given by: f(x)=- 3+x 2(2x-1)

5. (3 pts) Find a formula for the inverse function ƒ¯¹(x) if f(x)=- Solution 1 Write y=- where x = dom(f). 2x+3 4x-1 Step 1: Solve for x in terms of y: 2x+3 4x-1 2x+3 y= 4x-1 >> 4xy-y=2x+3 4xy-2x-3+y (0, 1, 2) 2x(2y-1)=3+y ⇒ x=- 3+y 2(2y-1) with (y #1/2). Step 2: Interchange x and y: y 3+x 2(2x-1) with x=1/2 Therefore, the formula for the inverse function of f is given by: f(x)= (0, 0.5,1) 3+x 2(2x-1) Solution 2 Write y=- where x = dom(f). 2x+3 4x-1 Step 1: Interchange x and y: x=. 2y+3 4y-1 with (y =1/4)" Step 2: Solve for y in terms of x: 2y+3 x=- 4y-1 4xy-x-2y+3 ⇒ 4xy-2y=3+x (0,1,2) 2y(2x-1)=3+xy= 3+x 2(2x-1) with (x=1/2). (0, 0.5,1) Therefore, the formula for the inverse function of ƒ is given by: f(x)=- 3+x 2(2x-1)

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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