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

The inverse of f(x)=(x+2)^{2/3}-4 is sqrt(x^3+12x^2+48x+64)-2,-sqrt(x^3+12x^2+48x+64)-2

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

inverse

x^{3} + 12 x^{2} + 48 x + 64 - 2, - x^{3} + 12 x^{2} + 48 x + 64 - 2

Solution steps

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

Replace

x

with

y

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

Solve for

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

x^{3} + 12 x^{2} + 48 x + 64 - 2, - x^{3} + 12 x^{2} + 48 x + 64 - 2

What is the inverse of f(x)=(x+2)^{2/3}-4 ?
The inverse of f(x)=(x+2)^{2/3}-4 is sqrt(x^3+12x^2+48x+64)-2,-sqrt(x^3+12x^2+48x+64)-2