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Omni-MATH / Consider functions f:[0,1]→R which satisfy

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Consider functions f:[0,1]→Rf : [0, 1] \rightarrow \mathbb{R} which satisfy (i) for all in , (ii) , (iii) whenever , , and are all in . Find, with proof, the smallest constant cc such that f(x)≤cxf(x) \le cx for every function ff satisfying (i)-(iii) and every xx in [0,1][0, 1] .
Plain-text mathematical notation (without MathML)
Consider functions f:[0,1]→R which satisfy
  (i) for all in ,    (ii) ,    (iii) whenever , , and are all in .
Find, with proof, the smallest constant c such that
f(x)≤cx
for every function f satisfying (i)-(iii) and every x in [0,1] .
Original LaTeX notation
Consider functions $f : [0, 1] \rightarrow \mathbb{R}$ which satisfy
  (i) for all in ,    (ii) ,    (iii) whenever , , and are all in .
Find, with proof, the smallest constant $c$ such that
$f(x) \le cx$
for every function $f$ satisfying (i)-(iii) and every $x$ in $[0, 1]$ .

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Source and history

task_id
a4f74911-c43d-54b0-9346-5d5be541cb44
task_key
test--a4f74911-c43d-54b0-9346-5d5be541cb44
task_revision_id
1
config / split
/ test

Official source

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