What is the inverse of f(x)=(x+4)^{(1/3)}-2 ?

The inverse of f(x)=(x+4)^{(1/3)}-2 is x^3+6x^2+12x+4

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inverse of f(x)=(x+4)^{(1/3)}-2

inverse

f (x) = (x + 4)^{(\frac{1}{3})} - 2

x^{3} + 6 x^{2} + 12 x + 4

Solution steps

y = (x + 4)^{\frac{1}{3}} - 2

Replace

x

with

y

x = (y + 4)^{\frac{1}{3}} - 2

Solve for

y, x = (y + 4)^{\frac{1}{3}} - 2

x^{3} + 6 x^{2} + 12 x + 4

f (y) = - 5 x + 9 y = - 18

f (x) = \frac{x}{x + 1}

x^{3} - 3 x^{2} + 3 x - 1

f (x) = \frac{x ^{2}}{x - 1}

4 x + 24

What is the inverse of f(x)=(x+4)^{(1/3)}-2 ?
The inverse of f(x)=(x+4)^{(1/3)}-2 is x^3+6x^2+12x+4