Question

Can someone please help me with this math problem

Answer 1

We have $f\left(f^{-1}(x)\right) = x$ for inverse functions $f(x)$ and $f^{-1}(x)$. Then if $f(x) = 2x+5$, we have

$f\left(f^{-1}(x)\right) = 2f^{-1}(x) + 5 = x \implies f^{-1}(x) = \dfrac{x-5}2$

Then

$f^{-1}(8) = \dfrac{8-5}2 = \boxed{\dfrac32}$