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

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

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inverse of f(x)=3x^2-2x+1

inverse

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

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

Solution steps

y = 3 x^{2} - 2 x + 1

Replace

x

with

y

x = 3 y^{2} - 2 y + 1

Solve for

y, x = 3 y^{2} - 2 y + 1

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

f (x) = (x + 1)^{2} - 2, x \geq - 1

f (x) = 4 + x - 2

f (x) = x + 2 + 5

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

f (x) = 2 (x + 3)^{2} - 5, x \leq - 3

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