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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

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