will give medal
Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.
f(x) = x3 + 4 and g(x) = Cube root of quantity x minus four.
if someone could show me how to get this with steps that would be amazing ;-)

Question

prussianmaster · Answer

what I would say here is that you should take the function f(x) and use that as your x values in the g(x) equation. Do the same for the other.

zzr0ck3r · Answer

Can you find the inverse of $f$ ?

hayisforhorses · Answer

So basically you are using function in place of x in order to solve for inverses. Begin with f(g(x)).
$$(\sqrt[3]{x-4})^{3} + 4$$   is what you would get when using g(x) as x.

hayisforhorses · Answer

Next, you do g(f(x)).$$\sqrt[3]{x^3+4-4}$$
Should be your answer.

hayisforhorses · Answer

Now, you simplify the results

hayisforhorses · Answer

In both, the 4 and -4 equal each other out along with the cube root and x^3. Therefore leaving you with a value of x for each one. Ergo, f(x) and g(x) are inverses.