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

The inverse of f(x)=x^2-3x-1 is (3+sqrt(4x+13))/2 ,(3-sqrt(4x+13))/2

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

inverse

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

\frac{3 + 4 x + 13}{2}, \frac{3 - 4 x + 13}{2}

Solution steps

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

Replace

x

with

y

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

Solve for

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

\frac{3 + 4 x + 13}{2}, \frac{3 - 4 x + 13}{2}

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

f (x) = x^{3} - 6 x^{2} + 9

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

f (x) = \frac{38}{41 - x}

f (x) = 3 - 2 x

What is the inverse of f(x)=x^2-3x-1 ?
The inverse of f(x)=x^2-3x-1 is (3+sqrt(4x+13))/2 ,(3-sqrt(4x+13))/2