Mathematics

Mathematics

Problem

a. Let f:R→Rf:\mathbb R\to\mathbb R be defined by f(x)=x2+af(x)=x^{2}+a where a∈Ra\in\mathbb R, and let g:(0,∞)→Rg:(0,\infty)\to\mathbb R be defined by g(x)=ln⁡xg(x)=\ln x. (i) Determine all real values of aa for which g∘fg\circ f is defined for every real xx. (ii) For such aa, state the domain of g∘fg\circ f. a. Let f:R→Rf:\mathbb R\to\mathbb R be defined by f(x)=x2+af(x)=x^{2}+a where a∈Ra\in\mathbb R, and let g:(0,∞)→Rg:(0,\infty)\to\mathbb R be defined by g(x)=ln⁡xg(x)=\ln x. (i) Determine all real values of aa for which g∘fg\circ f is defined for every real xx. (ii) For such aa, state the domain of g∘fg\circ f.

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