benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Does there exist a function f: mathbb R to mathbb R satisfying the following conditions: (i) for each real y there is a real x such that f(x)=y , and (ii) f(f(x))=(x−1)f(x)+2 for …

Problem

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

problem

Does there exist a function $f: \mathbb R \to \mathbb R $ satisfying the following conditions: (i) for each real yy there is a real xx such that f(x)=yf(x)=y , and (ii) f(f(x))=(x−1)f(x)+2f(f(x)) = (x - 1)f(x) + 2 for all real xx ?
Plain-text mathematical notation (without MathML)
Does there exist a function $f: \mathbb R \to \mathbb R $  satisfying the following conditions: 
(i) for each real y  there is a real  x such that f(x)=y , and 
(ii)  f(f(x))=(x−1)f(x)+2 for all real x ?
Original LaTeX notation
Does there exist a function $f: \mathbb R \to \mathbb R $  satisfying the following conditions: 
(i) for each real $y$  there is a real  $x$ such that $f(x)=y$ , and 
(ii)  $f(f(x)) = (x - 1)f(x) + 2$ for all real $x$ ?

Discussion

Discussion

No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

Source and history

task_id
0b4001c7-de3e-5e12-8b90-f2f10a90f7ec
task_key
test--0b4001c7-de3e-5e12-8b90-f2f10a90f7ec
task_revision_id
1
config / split
/ test

Official source

initial import