Question

Find the inverse of A(x) = x^1/5+5

Answer 1

In order to find the inverse of

`A(x)=x^{(1)/(5)}+5`

we first replace A(x) with y:

`y=x^{(1)/(5)}+5`

Then we replace every y with an x and every x with a y, like so:

`x=y^{(1)/(5)}+5`

We solve this new equation for y:

`x-5=y^{(1)/(5)}\Rightarrow y^{(1)/(5)}=x-5`

We raise both sides of the equation to the fifth power:

`(y^{(1)/(5)})^5=(x-5)^5`
`y=(x-5)^5`

Finally, we replace y with the inverse of the function:

`A^(-1)(x)=(x-5)^5`

and that is the inverse function.