Use composite of functions to determine whether f and g are inverses of one another.

f(x)=x^3+2; g(x)=cubed rt x-2

I am really having difficulties grasping this concept.

Question

Use composite of functions to determine whether f and g are inverses of one another.

f(x)=x^3+2; g(x)=cubed rt x-2

I am really having difficulties grasping this concept.

anonymous · Answer

You have to show that $f(g(x))=x$ and $g(f(x))=x$. Do you understand what a composite function is?

anonymous · Answer

yes, the function of a function. which is f(g(x)=cubed rt (x-2)^2+2

anonymous · Answer

Your notion of a composition is right, but
$$f(g(x))=f(\sqrt[3]{x-2})=\left(\sqrt[3]{x-2}\right)^3+2$$
Simplifying that, you should have it equal to $x$.

anonymous · Answer

thanks ... I did squared the cubed rt , instead of cubing it. Thanks.

anonymous · Answer

You're welcome. The work for $g(f(x))$ is pretty similar, I'll leave it to you.