91Ó°ÊÓ

Let \(f(x)=x^{2}+9, g(x)=\sqrt{x}\), and \(h(x)=g(f(x))\). Find the average rate of change of \(h\) over the following intervals. (a) \([-4,4]\) (b) \([0,4]\) (c) \([4,4+k]\)

Find \(h(x)=f(g(x))\) and \(j(x)=g(f(x)) .\) What are the domains of \(h\) and \(j\) ? $$ f(x)=x^{2}+9 \text { and } g(x)=\frac{1}{\sqrt{x}} $$

Find \(h(x)=f(g(x))\) and \(j(x)=g(f(x)) .\) What are the domains of \(h\) and \(j\) ? $$ f(x)=\frac{2}{x+2} \text { and } g(x)=x-2 $$

Find \(h(x)=f(g(x))\) and \(j(x)=g(f(x)) .\) What are the domains of \(h\) and \(j\) ? $$ f(x)=x^{2} \text { and } g(x)=-2 x+3 $$

Find \(h(x)=f(g(x))\) and \(j(x)=g(f(x)) .\) What are the domains of \(h\) and \(j\) ? $$ f(x)=\frac{x}{x-3} \text { and } g(x)=\frac{2}{x} $$

Find \((f+g)(x),(f g)(x)\), and \(\left(\frac{f}{g}\right)(x)\), and find their domains. $$ f(x)=a x+b \text { and } g(x)=c x+d $$

Find \((f+g)(x),(f g)(x)\), and \(\left(\frac{f}{g}\right)(x)\), and find their domains. $$ f(x)=3 x+2 \text { and } g(x)=5 x-1 $$

Find \((f+g)(x),(f g)(x)\), and \(\left(\frac{f}{g}\right)(x)\), and find their domains. $$ f(x)=2 x+3 \text { and } g(x)=x^{2}-1 $$

Find \((f+g)(x),(f g)(x)\), and \(\left(\frac{f}{g}\right)(x)\), and find their domains. $$ f(x)=\frac{3}{x+1} \text { and } g(x)=\frac{2 x}{x-5} $$

Find \((f+g)(x),(f g)(x)\), and \(\left(\frac{f}{g}\right)(x)\), and find their domains. $$ f(x)=\sqrt{x} \text { and } g(x)=\sqrt{x-3} $$