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

The inverse of f(x)= 1/2 x^2-x-3 is 1+sqrt(2x+7),1-sqrt(2x+7)

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

inverse

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

1 + 2 x + 7, 1 - 2 x + 7

Solution steps

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

Replace

x

with

y

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

Solve for

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

1 + 2 x + 7, 1 - 2 x + 7

f (x) = 8 x^{3} - 2

f (x) = \frac{x ^{3} + 8}{7}

f (x) = x - 3 + 2

f (x) = - 3 x + 12

f (x) = \frac{5}{4} cos (4 x + \frac{π}{2})

What is the inverse of f(x)= 1/2 x^2-x-3 ?
The inverse of f(x)= 1/2 x^2-x-3 is 1+sqrt(2x+7),1-sqrt(2x+7)