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

Answer:

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

Step-by-step 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 $f^{-1}x$

$x-5=2y$

$y=\frac{x-5}{2}$

$f^{-1}(x)=\frac{x-5}{2}$

Now substitute x=8, we get

$f^{-1}(8)=\frac{8-5}{2}=\frac{3}{2}$

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