Question

What is f^-1(3) when f(x) = (2x - 7)/3?

I've attached a photo of the question but I only need number two answered. 15 points, PLEASE HELP!!!

Answer 1

f^-1(3) =-1

Explanation:

f(x) = (2x - 7)/3

To find the inverse, we exchange x and y and solve for y

y = (2x - 7)/3

Exchange x and y

x = (2y - 7)/3

Solve for y

Multiply each side by 3

3x = (2y - 7)/3 *3

3x = 2y -7

Add 7 to each side

3x+7 = 2y-7+7

3x+7 = 2y

Divide by 2

(3x+7)/2 =2y/2

(3x+7)/2 =y

f^-1(x) =(3x+7)/2

We want to find this when x =-3

f^-1(3) =(3(-3)+7)/2

= (-9+7)/2

=-2/2

=-1