Question

Verify that the functions f and g, are inverses of each other by showing that f(g(x))=x and g(f(x0)=x.
f(x)=(x+2)^(3), g(x)=(3)√(x-2)

Answer 1

I think f(x) shoul dbe x^3+2

Answer 2

\[f\circ g(x)=f(g(x))=f(\sqrt[3]{x-2})=(\sqrt[3]{x-2}+2)^3\] so no they are not inverses. unless you meant what mandolino wrote

Answer 3

for your viewing pleasure

Answer 4

that was a typo srry
\[f(x)=(x+2)^3, g(x)=\sqrt[3]{x-2}\]

Answer 5

these are the functions that sat73 used, which are not inverses. i am suggesting that \[f(x)=x^3+2; \ \ g(x)=\sqrt[3]{x-2}\]are inverses of each other (see attached sketch above). i will show you the composition for these:\[f(g(x))=f(\sqrt[3]{x-2})=\left( \sqrt[3]{x-2} \right)^3+2=x-2+2=x\]and\[g(f(x))=g(x^3+2)=\sqrt[3]{(x^3+2)-2}=\sqrt[3]{x^3}=x\]thus f and g are inverse function of each other