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

Sagot :

Answer:

[tex] \hookrightarrow \: { \rm{f(x) = \frac{ {x}^{3} }{8} + 16}} \\ [/tex]

• let f(x) be m:

[tex]{ \rm{m = \frac{ {x}^{3} }{8} + 16}} \\ [/tex]

• make x the subject of the function:

[tex]{ \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)} }}[/tex]

• therefore:

[tex]{ \boxed{ \rm{ {f}^{ - 1} (x) = 2 {(m - 16)}^{ \frac{1}{3} } }} }\\ [/tex]

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