Question

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

Answer 1

In order to find the inverse of

$A(x)=x^{\frac{1}{5}}+5$

we first replace A(x) with y:

$y=x^{\frac{1}{5}}+5$

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

$x=y^{\frac{1}{5}}+5$

We solve this new equation for y:

$x-5=y^{\frac{1}{5}}\Rightarrow y^{\frac{1}{5}}=x-5$

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

$(y^{\frac{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.