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

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Answer:

[tex]f(x) = \frac{x + 1}{x} \\ let \: f ^{ - 1} (x) \: be \: k \\ k = \frac{x}{x + 1} \\ k(x + 1) = x \\ kx + k = x \\ kx - x = - k \\ x(k - 1) = - k \\ x = \frac{ - k}{k - 1} \\ x = \frac{k}{1 - k} \\ therefore \\ {f}^{ - 1} (x) = \frac{x}{1 - x} [/tex]

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