Question

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

Answer 1

I hope this helps you

Answer 2

`\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)`