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}

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