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

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

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inverse of f(x)=((3x)/2)^{2/3}+1

inverse

f (x) = (\frac{3 x}{2})^{\frac{2}{3}} + 1

\frac{2 ( x ^{3} - 3 x ^{2} + 3 x - 1 ) ^{\frac{1}{2}}}{3}, - \frac{2 ( x ^{3} - 3 x ^{2} + 3 x - 1 ) ^{\frac{1}{2}}}{3}

Solution steps

y = (\frac{3 x}{2})^{\frac{2}{3}} + 1

Replace

x

with

y

x = (\frac{3 y}{2})^{\frac{2}{3}} + 1

Solve for

y, x = (\frac{3 y}{2})^{\frac{2}{3}} + 1

\frac{2 ( x ^{3} - 3 x ^{2} + 3 x - 1 ) ^{\frac{1}{2}}}{3}, - \frac{2 ( x ^{3} - 3 x ^{2} + 3 x - 1 ) ^{\frac{1}{2}}}{3}

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