What is the inverse of 1/2 x^2-x-1 ?

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

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inverse of 1/2 x^2-x-1

inverse

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

1 + 2 x + 3, 1 - 2 x + 3

Solution steps

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

Replace

x

with

y

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

Solve for

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

1 + 2 x + 3, 1 - 2 x + 3

f (x) = \frac{5 x}{x + 1}

f (x) = x^{4} - x^{2}

f (x) = 6 x^{2} + 17

f (x) = ln (5 x^{4} + 12)

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