What is the inverse of f(x)=3x^2-x ?

The inverse of f(x)=3x^2-x is (1+sqrt(1+12x))/6 ,(1-sqrt(1+12x))/6

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inverse of f(x)=3x^2-x

inverse

f (x) = 3 x^{2} - x

\frac{1 + 1 + 12 x}{6}, \frac{1 - 1 + 12 x}{6}

Solution steps

y = 3 x^{2} - x

Replace

x

with

y

x = 3 y^{2} - y

Solve for

y, x = 3 y^{2} - y

\frac{1 + 1 + 12 x}{6}, \frac{1 - 1 + 12 x}{6}

- \frac{2}{x}

- \frac{1}{x}

(- 4, - 2), (- 2, 3)

- (x + 2) (x - 2) + 2 + x

y = \frac{1}{x ^{2} - 4}

What is the inverse of f(x)=3x^2-x ?
The inverse of f(x)=3x^2-x is (1+sqrt(1+12x))/6 ,(1-sqrt(1+12x))/6