What is the inverse of f(x)=2x^{1/3}+8 ?

The inverse of f(x)=2x^{1/3}+8 is (x^3)/8-3x^2+24x-64

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inverse of f(x)=2x^{1/3}+8

inverse

f (x) = 2 x^{\frac{1}{3}} + 8

\frac{x ^{3}}{8} - 3 x^{2} + 24 x - 64

Solution steps

y = 2 x^{\frac{1}{3}} + 8

Replace

x

with

y

x = 2 y^{\frac{1}{3}} + 8

Solve for

y, x = 2 y^{\frac{1}{3}} + 8

\frac{x ^{3}}{8} - 3 x^{2} + 24 x - 64

\frac{x ^{2} + 8 x + 16}{x + 4}

y = 2 x - 2

x^{3} + x^{2} - 4 x - 4

sin (3 x)

f (x) = \frac{- x - 5}{3}

What is the inverse of f(x)=2x^{1/3}+8 ?
The inverse of f(x)=2x^{1/3}+8 is (x^3)/8-3x^2+24x-64