What is the inverse of f(x)=\sqrt[3]{(3x-4)/2}+1 ?

The inverse of f(x)=\sqrt[3]{(3x-4)/2}+1 is (2x^3-6x^2+6x+2)/3

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inverse of f(x)=\sqrt[3]{(3x-4)/2}+1

inverse

\frac{2 x ^{3} - 6 x ^{2} + 6 x + 2}{3}

Solution steps

Replace

x

with

y

Solve for

\frac{2 x ^{3} - 6 x ^{2} + 6 x + 2}{3}

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

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

f (x) = x^{2} x^{2} - 9

f (x) = \frac{5 x}{3} + 5

f (x) = \frac{x ^{2} + 8 x + 15}{x + 3}

What is the inverse of f(x)=\sqrt[3]{(3x-4)/2}+1 ?
The inverse of f(x)=\sqrt[3]{(3x-4)/2}+1 is (2x^3-6x^2+6x+2)/3