What is the inverse of f(x)=5(x^{1/3}-8) ?

The inverse of f(x)=5(x^{1/3}-8) is (x^3}{125}+(24x^2)/(25)+\frac{192x)/5+512

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inverse of f(x)=5(x^{1/3}-8)

inverse

f (x) = 5 (x^{\frac{1}{3}} - 8)

\frac{x ^{3}}{125} + \frac{24 x ^{2}}{25} + \frac{192 x}{5} + 512

Solution steps

y = 5 (x^{\frac{1}{3}} - 8)

Replace

x

with

y

x = 5 (y^{\frac{1}{3}} - 8)

Solve for

y, x = 5 (y^{\frac{1}{3}} - 8)

\frac{x ^{3}}{125} + \frac{24 x ^{2}}{25} + \frac{192 x}{5} + 512

What is the inverse of f(x)=5(x^{1/3}-8) ?
The inverse of f(x)=5(x^{1/3}-8) is (x^3}{125}+(24x^2)/(25)+\frac{192x)/5+512