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

The inverse of f(x)=x+2/x is (x+sqrt(x^2-8))/2 ,(x-sqrt(x^2-8))/2

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

inverse

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

\frac{x + x ^{2} - 8}{2}, \frac{x - x ^{2} - 8}{2}

Solution steps

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

Replace

x

with

y

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

Solve for

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

\frac{x + x ^{2} - 8}{2}, \frac{x - x ^{2} - 8}{2}

What is the inverse of f(x)=x+2/x ?
The inverse of f(x)=x+2/x is (x+sqrt(x^2-8))/2 ,(x-sqrt(x^2-8))/2