Let be given by

MATHEMATICS · Subjective · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

Let f:R→Rf:\mathbb R\to \mathbb R be given by f(x)=x2+pf(x)=x^{2}+p, where p∈Rp\in\mathbb R. Let g:[0,∞)→Rg:[0,\infty)\to\mathbb R be defined by g(t)=tg(t)=\sqrt{t}. Determine all real values of pp for which the composition g∘fg\circ f is defined for every x∈Rx\in\mathbb R.

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