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## Homework Statement

Let ##f:R^+ \rightarrow R## be a strictly increasing function such that ##f(x) > -\frac{1}{x} \, \forall \,x>0## and ##\displaystyle f(x)f\left(f(x)+\frac{1}{x}\right)=1 \, \forall \, x>0##. Find

a. f(1)

b. Maximum value of f(x) in [1,2]

c. Minimum value of f(x) in [1,2]

## Homework Equations

## The Attempt at a Solution

Honestly, I don't know where to begin with. I think I need to somehow find f(x) but I don't see how. I am completely clueless. :(

Part b and c are easy once I have f(x).