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

Question

asked Mar 22, 2023 120k views

1 Answer

Ajoseps · Answer 1 · 2023-03-25T22:30:29+0000

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:

and that is the inverse function.