Question

What is the inverse of `h(x) = 5x + 2`?

Answer 1

`y = 1/5x - 2/5`

Explanation:

We have

`y = 5x+2`

When we invert a function what we are doing is reflecting it across the line `y=x` so what we do is swap the x and y in the function:

`x = 5y + 2`

`implies y = 1/5x - 2/5`

Answer 2

The inverse of a function `h(x)` is a function `f` such that the composition `h(f)=identity` or, in other words, such that `h(f(x))=x`

Explanation:

Given this definition, we apply `h` in the point `f(x)`; so `h(f(x))=5f(x)+2`. But this must be `h(f(x))=5f(x)+2=x` and hence `5(f(x))=x-2`, and then `f(x)=(x-2)/5=1/5x-2/5`