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:
[tex]f(x)=(x+7)^5[/tex]
So
[tex]y=(x+7)^5[/tex]
Changing x with y
[tex]x=(y+7_{})^5[/tex]
Now, we have to isolate y. So
[tex](y+7)^5=x[/tex]
We can apply the fifth root to both sides. So:
[tex]\sqrt[5]{(y+7)^5}=\sqrt[5]{x}[/tex][tex]y+7=\sqrt[5]{x}[/tex][tex]f^{-1}(x)=y=\sqrt[5]{x}-7[/tex]
