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) = \frac{x-5}2`

Then

`f^(-1)(8) = \frac{8-5}2 = \boxed{\frac32}`