What is the inverse of f(x)=6x^{1/3}-2 ?

The inverse of f(x)=6x^{1/3}-2 is (x^3)/(216)+(x^2)/(36)+x/(18)+1/27

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inverse of f(x)=6x^{1/3}-2

inverse

f (x) = 6 x^{\frac{1}{3}} - 2

\frac{x ^{3}}{216} + \frac{x ^{2}}{36} + \frac{x}{18} + \frac{1}{27}

Solution steps

y = 6 x^{\frac{1}{3}} - 2

Replace

x

with

y

x = 6 y^{\frac{1}{3}} - 2

Solve for

y, x = 6 y^{\frac{1}{3}} - 2

\frac{x ^{3}}{216} + \frac{x ^{2}}{36} + \frac{x}{18} + \frac{1}{27}

f (x) = \frac{4 x}{9 x - 1}

f (x) = 3 + 5 + 8 x

f (x) = 1 + 6 + 8 x

f (x) = 5 (0. 5^{- x})

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

What is the inverse of f(x)=6x^{1/3}-2 ?
The inverse of f(x)=6x^{1/3}-2 is (x^3)/(216)+(x^2)/(36)+x/(18)+1/27