If f(x) and f^-1(x) are inverse functions of each other and f(x)=2x+5, what is f^-1(8)

Question

asked May 13, 2017 173k views

2 Answers

David Hersey · Answer 1 · 2017-05-16T23:16:07+0000

Answer:

$\text{The value of }f^(-1)(8)\text{ is }(3)/(2)$

Explanation:

Given the function

f(x)=2x+5

$\text{we have to find the value of }f^(-1)(8)$

First we have to find the inverse

Step 1: Put f(x)=y, the equation becomes

y=2x+5

Step 2: Replace x to y and y to x, we get

x=2y+5

Step 3: Solve for y and then replace it with
f^(-1)x

x-5=2y

y=(x-5)/(2)

f^(-1)(x)=(x-5)/(2)

Now substitute x=8, we get

f^(-1)(8)=(8-5)/(2)=(3)/(2)

$\text{hence, the value of }f^(-1)(8)\text{ is }(3)/(2)$