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MATH / Let f(x) be a strictly increasing function defined for all x>0 such that f(x)>−(1)/(x) for all x>0, and f(x)f(f(x)+(1)/(x))=1for all x>0. Find f(1).

Problem

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problem

Let f(x)f(x) be a strictly increasing function defined for all x>0x > 0 such that f(x)>−1xf(x) > -\frac{1}{x} for all x>0x > 0, and f(x)f(f(x)+1x)=1f(x) f \left( f(x) + \frac{1}{x} \right) = 1for all x>0x > 0. Find f(1)f(1).
Plain-text mathematical notation (without MathML)
Let f(x) be a strictly increasing function defined for all x>0 such that f(x)>−(1)/(x) for all x>0, and
f(x)f(f(x)+(1)/(x))=1for all x>0.  Find f(1).
Original LaTeX notation
Let $f(x)$ be a strictly increasing function defined for all $x > 0$ such that $f(x) > -\frac{1}{x}$ for all $x > 0$, and
\[f(x) f \left( f(x) + \frac{1}{x} \right) = 1\]for all $x > 0$.  Find $f(1)$.

level

Level 5

type

Intermediate Algebra

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Source and history

task_id
72d35100-2ea8-532f-9bd2-5e788caf155d
task_key
intermediate~5falgebra--test--72d35100-2ea8-532f-9bd2-5e788caf155d
task_revision_id
1
config / split
intermediate_algebra / test

Official source

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