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

The inverse of f(x)=(x+3)^{1/3}-4 is x^3+12x^2+48x+61

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

inverse

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

x^{3} + 12 x^{2} + 48 x + 61

Solution steps

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

Replace

x

with

y

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

Solve for

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

x^{3} + 12 x^{2} + 48 x + 61

What is the inverse of f(x)=(x+3)^{1/3}-4 ?
The inverse of f(x)=(x+3)^{1/3}-4 is x^3+12x^2+48x+61