Question

Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.

f(x) = x^3 + 4 and g(x) = cube root of (x-4)

Answer 1

f(g(x)) = f(cube rootof (x-4)) = x - 4 + 4 = x

g(f(x)) = g(x^3+4) = cube root of (x^3+4-4) = cube root of x^3 = x

Answer 2

\[f(x)=x ^{3}+4\]\[g(x)=\sqrt[3]{x-4}\]To get f(g(x)), just put in g(x) wherever you see an x:\[f(g(x))=(\sqrt[3]{x-4})^{3}+4=(x-4)+4=x\]Do the same thing with g(f(x)):\[g(f(x))=\sqrt[3]{(x^{3}+4)-4}=\sqrt[3]{x ^{3}}\](Basically the same thing krandolph wrote, just a little easier to read).