Question

What is the inverse of the function g(x) = x^3/8 + 16 ?

Answer 1

`\hookrightarrow \: { \rm{f(x) = \frac{ {x}^(3) }{8} + 16}} \\`

• let f(x) be m:

`{ \rm{m = \frac{ {x}^(3) }{8} + 16}} \\`

• make x the subject of the function:

`{ \rm{8m = {x}^(3) + 128}} \\ \\ { \rm{ {x}^(3) = 8m - 128 }} \\ \\ { \rm{ {x}^(3) = 8(m - 16) }} \\ \\ { \rm{x = \sqrt[3]{8} * \sqrt[3]{(m - 16)} }} \\ \\ { \rm{x = 2 \sqrt[3]{(m - 16)} }}`

• therefore:

`{ \boxed{ \rm{ {f}^( - 1) (x) = 2 {(m - 16)}^{ (1)/(3) } }} }\\`