Question

What is the inverse function f(x) = 2x-10?

Answer 1

If
`f^(-1)(x)` is the inverse of
`f(x)`, then by definition of inverse function,

`f\left(f^(-1)(x)\right) = x`

so that

`f\left(f^(-1)(x)\right) = 2f^(-1)(x)-10 = x`

Solve for the inverse:

`2f^(-1)(x) - 10 = x \\\\ 2f^(-1)(x) = x+10 \\\\ \boxed{f^(-1)(x) = \frac x2 + 5}`