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

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

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

inverse

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

f (x) = - 4 x - 3

f (x) = x + 36

f (x) = (x^{2} + 6 x)^{\frac{1}{2}}

f (x) = 2 x^{5} - 7

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