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

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

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

inverse

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

- 1 + 2 x, - 2 x - 1

Solution steps

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

Replace

x

with

y

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

Solve for

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

- 1 + 2 x, - 2 x - 1

f (x) = \frac{1}{9} x + 5

f (x) = \frac{( 5 x + 8 )}{( 6 x - 10 )}

f (x) = 11 + 4 x - 4

\frac{1}{\frac{1}{2} ( x - 2 )}

f (x) = ln (7 x + e)

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