What is the inverse of f(x)=10x^{1/3}-9 ?

The inverse of f(x)=10x^{1/3}-9 is (x^3)/(1000)+(27x^2)/(1000)+(243x)/(1000)+729/1000

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inverse of f(x)=10x^{1/3}-9

inverse

f (x) = 10 x^{\frac{1}{3}} - 9

\frac{x ^{3}}{1000} + \frac{27 x ^{2}}{1000} + \frac{243 x}{1000} + \frac{729}{1000}

Solution steps

y = 10 x^{\frac{1}{3}} - 9

Replace

x

with

y

x = 10 y^{\frac{1}{3}} - 9

Solve for

y, x = 10 y^{\frac{1}{3}} - 9

\frac{x ^{3}}{1000} + \frac{27 x ^{2}}{1000} + \frac{243 x}{1000} + \frac{729}{1000}

f (x) = (x - 3)^{2}

\frac{x - 1}{x ^{2}}

f (x) = x^{2} + 3 x - 4

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

f (x) = \frac{2 x + 5}{x}

What is the inverse of f(x)=10x^{1/3}-9 ?
The inverse of f(x)=10x^{1/3}-9 is (x^3)/(1000)+(27x^2)/(1000)+(243x)/(1000)+729/1000