What is the inverse of f(x)=4\sqrt[3]{x}-3 ?

The inverse of f(x)=4\sqrt[3]{x}-3 is (x^3)/(64)+(9x^2)/(64)+(27x)/(64)+27/64

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inverse of f(x)=4\sqrt[3]{x}-3

inverse

f (x) = 4 3 x - 3

\frac{x ^{3}}{64} + \frac{9 x ^{2}}{64} + \frac{27 x}{64} + \frac{27}{64}

Solution steps

y = 4 3 x - 3

Replace

x

with

y

x = 4 3 y - 3

Solve for

y, x = 4 3 y - 3

\frac{x ^{3}}{64} + \frac{9 x ^{2}}{64} + \frac{27 x}{64} + \frac{27}{64}

y = \frac{3 - 2 x}{2 x - 5}

y = 9^{2} - 5

y = 3^{x - 1}

2 ln (\frac{x}{2} + 1)

y = 3^{x - 2}

What is the inverse of f(x)=4\sqrt[3]{x}-3 ?
The inverse of f(x)=4\sqrt[3]{x}-3 is (x^3)/(64)+(9x^2)/(64)+(27x)/(64)+27/64