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f (x+1 )=1+f(x) and f (x^4-x^2 )=f^4(x)-f^2(x)

Source: SRMC 2018 P2

September 1, 2018
functional equationalgebra

Problem Statement

Find all functions f: R→Rf:\ \mathbb{R}\rightarrow\mathbb{R} such that for any real number xx the equalities are true: f(x+1)=1+f(x)f\left(x+1\right)=1+f(x) and f(x4−x2)=f4(x)−f2(x).f\left(x^4-x^2\right)=f^4(x)-f^2(x).
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