perplexus.info :: Just Math : Function Inequalities

Function Inequalities (Posted on 2025-03-18)

Let f be a function defined on all real numbers such that for all x, we have f(x + 5) ≥ f(x) + 5, and f(x + 1) ≤ f(x) + 1. If f(1) = 1, find f(2025).

No Solution Yet Submitted by Danish Ahmed Khan

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re: Unsolvable

| Comment 4 of 5 |

(In reply to Unsolvable by Jer)

Where did f(7)<=6 come from? Since f(6)=6, wouldn't rule 2 say f(7)<=7 (one more than f(6)? ... and rule 1 say f(7)>=7 based on f(2) being 2? Therefore f(7)=7.

Posted by Charlie on 2025-03-19 07:11:07

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