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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

y = 3 x - 6

e^{x} - 9

f (x) = 5 x + 20

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