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

The inverse of f(x)=2+\sqrt[3]{2-3x} is -(x^3-6x^2+12x-10)/3

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

inverse

- \frac{x ^{3} - 6 x ^{2} + 12 x - 10}{3}

Solution steps

Replace

x

with

y

Solve for

- \frac{x ^{3} - 6 x ^{2} + 12 x - 10}{3}

y = \frac{4 x ^{2} - 5}{2 x ^{3} + x}

f (x) = \frac{- x ^{2} + 25}{4 x + 20}

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

f (x) = (x + 7)^{3} - 7

6 lo g_{3} (5 x + 6)

What is the inverse of f(x)=2+\sqrt[3]{2-3x} ?
The inverse of f(x)=2+\sqrt[3]{2-3x} is -(x^3-6x^2+12x-10)/3