Question

when solving this, do i take it out of the parenthesis or make it into a square root? because its very confusing.

Answer 1

Finding the inverse function:

We are given a function y = f(x). To find the inverse function, we exchange x with y in the original function, and then isolate y.

So

We are given the function:

$f(x)=(x+7)^5$

So

$y=(x+7)^5$

Changing x with y

$x=(y+7_{})^5$

Now, we have to isolate y. So

$(y+7)^5=x$

We can apply the fifth root to both sides. So:

$\sqrt[5]{(y+7)^5}=\sqrt[5]{x}$$y+7=\sqrt[5]{x}$$f^{-1}(x)=y=\sqrt[5]{x}-7$