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

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

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

inverse

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

\frac{- 1 + x + x ^{2} - 2 x - 3}{2}, \frac{- 1 + x - x ^{2} - 2 x - 3}{2}

Solution steps

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

Replace

x

with

y

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

Solve for

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

\frac{- 1 + x + x ^{2} - 2 x - 3}{2}, \frac{- 1 + x - x ^{2} - 2 x - 3}{2}

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