Library / /9 of 22
Algebra Difficulty 5.2 AIME, harder Prove it Belarus
Does there exist a function f(x):R→R satisfying the equality
f(∣x∣)+∣f(x)∣=x
for all real numbers x?
Solution
Answer: no, such function doesn't exist.
Looking for a route rather than an archive?
The track puts 2,000
problems in a working order, from AMC 10 level to the IMO shortlist.
Source: MathNet,
licensed CC-BY-4.0.
Statement and solution reproduced as published; topic and difficulty added by this site.