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Find all reals a

Source: India Postal Set 6 P 3 2016

January 18, 2017
functionfunctional equationalgebra

Problem Statement

Find all real numbers aa such that there exists a function f:R→Rf:\mathbb R\to \mathbb R such that the following conditions are simultaneously satisfied: (a) f(f(x))=xf(x)−ax,  ∀x∈R;f(f(x))=xf(x)-ax,\;\forall x\in\mathbb{R}; (b) ff is not a constant function; (c) ff takes the value aa.
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