What is the inverse of f(x)=x+1/x ,x>0 ?

The inverse of f(x)=x+1/x ,x>0 is (x+sqrt(x^2-4))/2 ,(x-sqrt(x^2-4))/2

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inverse of f(x)=x+1/x ,x>0

inverse

f (x) = x + \frac{1}{x}, x > 0

\frac{x + x ^{2} - 4}{2}, \frac{x - x ^{2} - 4}{2}

Solution steps

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

Replace

x

with

y

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

Solve for

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

\frac{x + x ^{2} - 4}{2}, \frac{x - x ^{2} - 4}{2}

What is the inverse of f(x)=x+1/x ,x>0 ?
The inverse of f(x)=x+1/x ,x>0 is (x+sqrt(x^2-4))/2 ,(x-sqrt(x^2-4))/2