Question

How do you find the inverse of `f(x)=root5(5x+4)`?

Answer 1

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

Explanation:

Let `y = f(x): y = root(5)(5x+4)`

Swap `y` for `x` and `x` for `y`: `x = root(5)(5y+4)`

Remember that `root(5)( ) = ( )^(1/5)` so `x = (5y+4)^(1/5)`

Solve for `y`.

1. 5th power both sides: `x^5 = ((5y+4)^(1/5))^5 = 5y+4`
2. Isolate `y`: `5y = x^5-4`
3. Simplify: `y = (x^5-4)/5`

The inverse function `f^-1 = (x^5-4)/5`