What is the inverse of f(x)=(x^2-4)^{5/3} ?

The inverse of f(x)=(x^2-4)^{5/3} is sqrt(x^{3/5)+4},-sqrt(x^{3/5)+4}

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inverse of f(x)=(x^2-4)^{5/3}

inverse

f (x) = (x^{2} - 4)^{\frac{5}{3}}

x^{\frac{3}{5}} + 4, - x^{\frac{3}{5}} + 4

Solution steps

y = (x^{2} - 4)^{\frac{5}{3}}

Replace

x

with

y

x = (y^{2} - 4)^{\frac{5}{3}}

Solve for

y, x = (y^{2} - 4)^{\frac{5}{3}}

x^{\frac{3}{5}} + 4, - x^{\frac{3}{5}} + 4

What is the inverse of f(x)=(x^2-4)^{5/3} ?
The inverse of f(x)=(x^2-4)^{5/3} is sqrt(x^{3/5)+4},-sqrt(x^{3/5)+4}