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

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

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

inverse

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

\frac{x + x ^{2} + 3}{3}, \frac{x - x ^{2} + 3}{3}

Solution steps

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

Replace

x

with

y

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

Solve for

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

\frac{x + x ^{2} + 3}{3}, \frac{x - x ^{2} + 3}{3}

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