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

The inverse of f(x)=(1-x^2)^{-1/3} is sqrt(-(1-x^3)/(x^3)),-sqrt(-(1-x^3)/(x^3))

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

inverse

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

- \frac{1 - x ^{3}}{x ^{3}}, - - \frac{1 - x ^{3}}{x ^{3}}

Solution steps

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

Replace

x

with

y

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

Solve for

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

- \frac{1 - x ^{3}}{x ^{3}}, - - \frac{1 - x ^{3}}{x ^{3}}

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