Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x
$$f(x)=x^3+4$$$$g(x)=\sqrt[3]{x-4}$$

Question

turingtest · Answer

have you tried anything yet?

anonymous · Answer

yeah i tried plugging it in but i couldn't understand and ended up confusing myself

turingtest · Answer

can you try to show what you did?
...or at least the first step?

anonymous · Answer

sorry my computer is acting up what idid was f(g(x))=  Cube root of quantity x minus four + 4

turingtest · Answer

f(g(x)) will have f on the outside, but you have the cube root, which is in g, on the outside

turingtest · Answer

$$f(g(x))=[g(x)]^3+4=\left(\sqrt[3]{x^2-4}\right)^3+4$$simplify and do the same for g(f(x))

anonymous · Answer

but how you Confirm that f and g are inverses by showing that

anonymous · Answer

how does that equal x

turingtest · Answer

well, what is$$\sqrt{x^2}$$ simplified to?

turingtest · Answer

or rather, $$(\sqrt x)^2$$(which simplifies tothe same thing

anonymous · Answer

it not x^2 but but just x from the problem above that you solve sorry

turingtest · Answer

There is an x under the cube root, but I am merely illustrating a point with a related example. if you could just bear with me, you'll see where i'm going with this.I will cahnge symbols to avoid confusion:
simply$$(\sqrt n)^2$$what do you get?

turingtest · Answer

simplify*

anonymous · Answer

thank you

anonymous · Answer

i understand

turingtest · Answer

ok, you're welcome