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

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

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

inverse

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

\frac{2 \cdot 2 ^{\frac{1}{2}}}{x ^{\frac{3}{2}}}, - \frac{2 \cdot 2 ^{\frac{1}{2}}}{x ^{\frac{3}{2}}}

Solution steps

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

Replace

x

with

y

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

Solve for

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

\frac{2 \cdot 2 ^{\frac{1}{2}}}{x ^{\frac{3}{2}}}, - \frac{2 \cdot 2 ^{\frac{1}{2}}}{x ^{\frac{3}{2}}}

f (x) = (x + 2)

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

f (x) = 8 x^{2} + 3

f (x) = x + \frac{1}{x}, x > 0

4 + x + 9

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