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

The inverse of f(x)=5x^{1/3}-1 is (x^3)/(125)+(3x^2)/(125)+(3x)/(125)+1/125

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

inverse

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

\frac{x ^{3}}{125} + \frac{3 x ^{2}}{125} + \frac{3 x}{125} + \frac{1}{125}

Solution steps

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

Replace

x

with

y

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

Solve for

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

\frac{x ^{3}}{125} + \frac{3 x ^{2}}{125} + \frac{3 x}{125} + \frac{1}{125}

\frac{2 x ^{2} + 18}{x}

(9, - 9), (3, 3)

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

(2, 0), (0, 6)

- \frac{7 x}{6 x - 5}

What is the inverse of f(x)=5x^{1/3}-1 ?
The inverse of f(x)=5x^{1/3}-1 is (x^3)/(125)+(3x^2)/(125)+(3x)/(125)+1/125