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

The inverse of f(x)=2x^{2/5} is (x^{5/2})/(4*2^{1/2)},-(x^{5/2})/(4*2^{1/2)}

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

inverse

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

\frac{x ^{\frac{5}{2}}}{4 \cdot 2 ^{\frac{1}{2}}}, - \frac{x ^{\frac{5}{2}}}{4 \cdot 2 ^{\frac{1}{2}}}

Solution steps

y = 2 x^{\frac{2}{5}}

Replace

x

with

y

x = 2 y^{\frac{2}{5}}

Solve for

y, x = 2 y^{\frac{2}{5}}

\frac{x ^{\frac{5}{2}}}{4 \cdot 2 ^{\frac{1}{2}}}, - \frac{x ^{\frac{5}{2}}}{4 \cdot 2 ^{\frac{1}{2}}}

f (x) = \frac{- x + 4}{5}

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

f (x) = \frac{10}{x - 4}

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

f (x) = (5 x - 4)^{2} + 2

What is the inverse of f(x)=2x^{2/5} ?
The inverse of f(x)=2x^{2/5} is (x^{5/2})/(4*2^{1/2)},-(x^{5/2})/(4*2^{1/2)}