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

The inverse of f(x)=(x+2)^{1/3}+2 is x^3-6x^2+12x-10

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

inverse

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

x^{3} - 6 x^{2} + 12 x - 10

Solution steps

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

Replace

x

with

y

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

Solve for

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

x^{3} - 6 x^{2} + 12 x - 10

f (x) = \frac{1}{4 x}

∣ x ∣ - 5

5 x - 3 y = - 15

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

- x^{2} - 1

What is the inverse of f(x)=(x+2)^{1/3}+2 ?
The inverse of f(x)=(x+2)^{1/3}+2 is x^3-6x^2+12x-10