91Ó°ÊÓ

In \(8-13\) , the domain of \(f(x)=4-2 x\) and of \(g(x)=x^{2}\) is the set of real numbers and the domain of \(h(x)=\frac{1}{x}\) is the set of non-zero real numbers. a. Write each function value in terms of \(x\) . b. Find the domain of each function. \((\mathrm{gh})(x)\)

\(\operatorname{In} 9-14, y=f(x) .\) Find \(f(-3)\) for each function. \(y=1+x^{2}\)

In \(11-18 :\) a. Find \(h(x)\) when \(h(x)=g(f(x)) .\) b. What is the domain of \(h(x) ?\) c. What is the range of \(\mathrm{h}(x) ?\) d. Graph \(\mathrm{h}(x)\) $$ \mathrm{f}(x)=2 x+1, \mathrm{g}(x)=4 x $$

In \(8-13\) , the domain of \(f(x)=4-2 x\) and of \(g(x)=x^{2}\) is the set of real numbers and the domain of \(h(x)=\frac{1}{x}\) is the set of non-zero real numbers. a. Write each function value in terms of \(x\) . b. Find the domain of each function. \(\left(\frac{g}{f}\right)(x)\)

In \(6-12,\) tell whether the variables vary directly, inversely, or neither. Each day, I am awake \(a\) hours and I sleep \(s\) hours.

In \(11-16,\) determine if the function has an inverse. If so, list the pairs of the inverse function. If not, explain why there is no inverse function. $$ \\{(0,8),(1,7),(2,6),(3,5),(4,4)\\} $$

\(A(2,7)\) is a fixed point in the coordinate plane. Let \(B(x, 7)\) be any point on the same horizontal line. If \(A B=\mathrm{h}(x),\) express \(\mathrm{h}(x)\) in terms of \(x .\)

In \(11-16,\) determine if the function has an inverse. If so, list the pairs of the inverse function. If not, explain why there is no inverse function. $$ \\{(1,4),(2,7),(1,10),(4,13)\\} $$

In \(12-17,\) use a graph to find the solution set of each inequality. $$ x^{2}+2 x-3 < 0 $$

In \(11-18 :\) a. Find \(h(x)\) when \(h(x)=g(f(x)) .\) b. What is the domain of \(h(x) ?\) c. What is the range of \(\mathrm{h}(x) ?\) d. Graph \(\mathrm{h}(x)\) $$ f(x)=3 x, g(x)=x-1 $$