Question

How do you find the inverse of `f(x) = 4(x + 5)^2 - 6`?

Answer 1

`f^(-1)(x)=(sqrt((x+6)/4))-5`

Explanation:

Let `y=4(x+5)^2-6`, swap the letters `x and y` and then rearrange to make `y` the subject.

`x=4(y+5)^2-6`

`x+6=4(y+5)^2`

`(x+6)/4=(y+5)^2`

`sqrt((x+6)/4)=y+5`

`(sqrt((x+6)/4))-5=y`