What is the inverse of f(x)=\sqrt[3]{x-1}-2 ?

The inverse of f(x)=\sqrt[3]{x-1}-2 is x^3+6x^2+12x+9

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inverse of f(x)=\sqrt[3]{x-1}-2

inverse

x^{3} + 6 x^{2} + 12 x + 9

Solution steps

Replace

x

with

y

Solve for

x^{3} + 6 x^{2} + 12 x + 9

x^{2} + 8 x + 14

f (x) = \frac{y - 10}{y ^{2} + 3}

12 x + 3 y = - 18

\frac{x + 2}{x ^{3} + 8}

f (x) = \frac{2 x - 4}{3}

What is the inverse of f(x)=\sqrt[3]{x-1}-2 ?
The inverse of f(x)=\sqrt[3]{x-1}-2 is x^3+6x^2+12x+9