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

The inverse of f(x)=(x^{1/3}+2)/(x^{1/3)-2} is (8+24x+24x^2+8x^3)/(x^3-3x^2+3x-1)

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

inverse

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

\frac{8 + 24 x + 24 x ^{2} + 8 x ^{3}}{x ^{3} - 3 x ^{2} + 3 x - 1}

Solution steps

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

Replace

x

with

y

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

Solve for

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

\frac{8 + 24 x + 24 x ^{2} + 8 x ^{3}}{x ^{3} - 3 x ^{2} + 3 x - 1}

What is the inverse of f(x)=(x^{1/3}+2)/(x^{1/3)-2} ?
The inverse of f(x)=(x^{1/3}+2)/(x^{1/3)-2} is (8+24x+24x^2+8x^3)/(x^3-3x^2+3x-1)