Question

How do you find the inverse of `f(x) =1/4x+7`?

Answer 1

Write `y = 1/4x+7`

then rearrange to find `x = 4(y-7)`, so the inverse function is:

`f^-1(y) = 4(y-7)`

Explanation:

Let `y = f(x) = 1/4x+7`

Subtract `7` from both ends to get:

`y-7 = 1/4x`

Multiply both sides by `4` to get:

`x = 4(y-7)`

This defines `x` in terms of `y` in such a way that the equation `y = 1/4x+7` is satisfied, so it defines the inverse function:

`f^-1(y) = 4(y-7)`