Question

Please help me answer this question thank you :)

Answer 1

A.

`f(x) = \frac{ \sqrt[3]{x} }{5} \: { \bf{and}} \: g(x) = 5 {x}^(3)`

Explanation:

Consider f(x) as the original function:

`{ \tt{f(x) = \frac{ \sqrt[3]{x} }{5} }}`

Let the inverse be m:

`{ \tt{g(x) = f {}^( - 1) (x) = m}} \\ { \tt{m = \frac{ \sqrt[3]{x} }{5} }} \\ { \tt{5m = \sqrt[3]{x} }} \\ { \tt{x = 5m {}^(3) }} \\ therefore : \\ { \tt{g(x) = 5 {x}^(3) }}`