EXERCISE SOLUTION-0.2, Pag#24, Calculus Book

Q.32 Solution:  $$f(x)=\sqrt{x-3}, g(x)=\sqrt{x^{2}+3}$$ Domain of $f$ consists of all real numbers $x$ such that $x-3 \geq 0 \Rightarrow x \geq 3$ or $[3, \infty)$ Range of $f:[0, \infty)$ Domain of $g$ : All real numbers or $(-\infty, \infty)$ $$(f \circ g)(x)=f(g(x))$$ $$=f\left(\sqrt{x^{2}+3}\right)=\sqrt{\sqrt{x^{2}+3}-3}$$ $$(f \circ g)(x)=\sqrt{\sqrt{x^{2}+3}-3}$$ Domain of $f$ og: for all $x \geq \sqrt{6}$ … Read more