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

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

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

inverse

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

2 x + 2, - 2 x + 2

Solution steps

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

Replace

x

with

y

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

Solve for

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

2 x + 2, - 2 x + 2

f (x) = \frac{5 x ^{3} + 4 x - 2}{4 x}

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

f (x) = 6 x - x^{2}

- x^{3} + 8 x^{2} - 15 x

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

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