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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

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