91Ó°ÊÓ

$$ \text { Factor the polynomials in Exercises } \text { . } $$ $$ 5+12 x-3 x^{2} $$

Let \(f(x)=\frac{x}{x-2}, g(x)=\frac{5-x}{5+x}\), and \(h(x)=\frac{x+1}{3 x-1}\). Express the following as rational functions. $$ f(x+2)+g(x+2) $$

Response of a Muscle When a solution of acetylcholine is introduced into the heart muscle of a frog, it diminishes the force with which the muscle contracts. The data from experiments of the biologist A. J. Clark are closely approximated by a function of the form $$ R(x)=\frac{100 x}{b+x}, \quad x \geq 0 $$ where \(x\) is the concentration of acetyleholine (in appropriate units), \(b\) is a positive constant that depends on the particular frog, and \(R(x)\) is the response of the muscle to the acetylcholine, expressed as a percentage of the maximum possible effect of the drug. (a) Suppose that \(b=20\). Find the response of the muscle when \(x=60\). (b) Determine the value of \(b\) if \(R(50)=60\), that is, if a concentration of \(x=50\) units produces a \(60 \%\) response.

$$ \text { Factor the polynomials in Exercises } \text { . } $$ $$ 15+12 x-3 x^{2} $$

Right to Drill A gas company will pay a property owner \(\$ 5000\) for the right to drill on his land for natural gas and \(\$ .10\) for each thousand cubic feet of gas extracted from the land. Express the amount of money the landowner will receive as a function of the amount of gas extracted from the land.

In Exercises \(1-28\), compute the numbers. $$ (27)^{2 / 3} $$

Let \(f(x)=\frac{x}{x-2}, g(x)=\frac{5-x}{5+x}\), and \(h(x)=\frac{x+1}{3 x-1}\). Express the following as rational functions. $$ \frac{g(x+5)}{f(x+5)} $$

In Exercises \(21-28\), describe the domain of the function. $$ f(x)=\frac{8 x}{(x-1)(x-2)} $$

$$ \text { Factor the polynomials in Exercises } \text { . } $$ $$ 3 x-x^{2} $$

Compute the numbers. \((1.8)^{0}\)