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

The inverse of f(x)=2x^{1/3}+3 is (x^3)/8-(9x^2)/8+(27x)/8-27/8

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

inverse

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

\frac{x ^{3}}{8} - \frac{9 x ^{2}}{8} + \frac{27 x}{8} - \frac{27}{8}

Solution steps

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

Replace

x

with

y

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

Solve for

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

\frac{x ^{3}}{8} - \frac{9 x ^{2}}{8} + \frac{27 x}{8} - \frac{27}{8}

12 x + 5 y = - 18

x^{3} - x + 1

- \frac{1}{( x - 5 ) ^{4}}

f (x) = 4 π r^{2}

\frac{- 2 x + 63}{x ( x + 9 )}

What is the inverse of f(x)=2x^{1/3}+3 ?
The inverse of f(x)=2x^{1/3}+3 is (x^3)/8-(9x^2)/8+(27x)/8-27/8