Question

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

Answer 1

Answer:

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

• let f(x) be m:

${ \rm{m = \frac{ {x}^{3} }{8} + 16}}$

• make x the subject of the function:

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

• therefore:

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