How do you show f(x)=5x^3 and g(x) the cube root of x/5 are inverses?

Question

anonymous · Answer

compute f(g(x)) and g(f(x)) and then see both are equal to x.
Then you can conclude the required result.@dtan5457

dtan5457 · Answer

How do you simplify cube roots again?

dtan5457 · Answer

So If I put cube root of 5x^3/5

dtan5457 · Answer

I know for this one i just remove the ^3 from 5x and get x

dtan5457 · Answer

What about one with like ^2

anonymous · Answer

do you know what is f(g(x))??

solomonzelman · Answer

$\large\color{black}{\color{red}{f(x)}=5\color{green}{x}^3 }$
$\large\color{black}{\color{red}{y}=5\color{green}{x}^3 }$
$\large\color{black}{\color{green}{x}=5\color{red}{y}^3 }$
Solve for y....

solomonzelman · Answer

dtan, you solution of y, continuing from where I was going, would be the inverse function, $\large\color{black}{f^{-1}x }$.

mertsj · Answer

Find f(g(x)
Find g(f(x)
If you get x in both cases then they are inverse functions.

dtan5457 · Answer

When I plug them in. Does the cube root of 5x^3/5 equal x?