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

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

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

inverse

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

\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}

\frac{2 x ( x - 1 ) ^{2}}{( x + 1 ) ^{3}}

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

f (x) = \frac{1}{x - 6}

(3, 4.6904), (0, 0)

f (x) = \frac{x ^{2} - x - 2}{x - 3}

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