Question

find f(g(x)) and g(f(x))
f(x)=x^2/3
g(x)=x^6

I know the answer is x^4 for both, but I don't understand why it is x^4. Can someone explain?

Answer 1

To find the answer for each, you just have to plug one equation into the other, and then multiply the exponents
\[f(g(x))=(x^{6})^{2/3} = x ^{6*2/3} = x ^{4}\] and the same steps can be followed to find g(f(x))