f-x-is-a-strictly-monotonic-function-in-its-domain-0-such-that-x-gt-0-f-f-x-1-x-2-Find-f-x-

Question Number 181599 by CrispyXYZ last updated on 27/Nov/22

f (x) is a strictly monotonic function in its domain (0, + \infty)

such that \forall x > 0, f (f (x) - \frac{1}{x}) = 2 .

Find f (x) .

Answered by mr W last updated on 27/Nov/22

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

f (t) = 2

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

f (t) = t + \frac{1}{t} = 2

t^{2} - 2 t + 1 = 0 \Rightarrow t = 1

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

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