What is the inverse of f(x)=0.4x^{2/3} ?

The inverse of f(x)=0.4x^{2/3} is (5*5^{1/2}x^{3/2})/(2*2^{1/2)},-(5*5^{1/2}x^{3/2})/(2*2^{1/2)}

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inverse of f(x)=0.4x^{2/3}

inverse

f (x) = 0.4 x^{\frac{2}{3}}

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

Solution steps

y = 0.4 x^{\frac{2}{3}}

Replace

x

with

y

x = 0.4 y^{\frac{2}{3}}

Solve for

y, x = 0.4 y^{\frac{2}{3}}

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

What is the inverse of f(x)=0.4x^{2/3} ?
The inverse of f(x)=0.4x^{2/3} is (5*5^{1/2}x^{3/2})/(2*2^{1/2)},-(5*5^{1/2}x^{3/2})/(2*2^{1/2)}