Let and .…

MATHEMATICS · Single correct · CBSE · Mathematics · Polynomials · Polynomials

Problem

Let f(x)=x2−2xf(x)=x^2-2x and g(x)=f(f(x)−1)+f(5−f(x))g(x)=f(f(x)-1)+f(5-f(x)). Then (1) g(x)<0g(x)<0 for all x∈Rx\in\mathbb{R} (2) g(x)<0g(x)<0 for some x∈Rx\in\mathbb{R} (3) g(x)≥0g(x)\geq0 for some x∈Rx\in\mathbb{R} (4) g(x)≥0g(x)\geq0 for all x∈Rx\in\mathbb{R}

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