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

The inverse of f(x)=3x^{-2/5} is (9*3^{1/2})/(x^{5/2)},-(9*3^{1/2})/(x^{5/2)}

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

inverse

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

\frac{9 \cdot 3 ^{\frac{1}{2}}}{x ^{\frac{5}{2}}}, - \frac{9 \cdot 3 ^{\frac{1}{2}}}{x ^{\frac{5}{2}}}

Solution steps

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

Replace

x

with

y

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

Solve for

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

\frac{9 \cdot 3 ^{\frac{1}{2}}}{x ^{\frac{5}{2}}}, - \frac{9 \cdot 3 ^{\frac{1}{2}}}{x ^{\frac{5}{2}}}

f (x) = \frac{7}{2 x + 5}

\frac{2 - x}{3 + x}

\frac{2 x}{5 - x}

f (x) = 38 - 1.25 x

h (x) = - 2 x + 5

What is the inverse of f(x)=3x^{-2/5} ?
The inverse of f(x)=3x^{-2/5} is (9*3^{1/2})/(x^{5/2)},-(9*3^{1/2})/(x^{5/2)}