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Chapter 1: Problem 58
Find the domain of the function. $$g(x)=1-2 x^{2}$$
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Prove that the product of two odd functions is an even function, and that the product of two even functions is an even function.
Determine whether the equation represents \(y\) as a function of \(x .\) $$x^{2}+y=5$$
Your wage is \(\$ 12.00\) per hour plus \(\$ 0.55\) for each unit produced per hour. So, your hourly wage \(y\) in terms of the number of units produced \(x\) is \(y=12+0.55 x.\) (a) Find the inverse function. What does each variable in the inverse function represent? (b) Use a graphing utility to graph the function and its inverse function. (c) Use the trace feature of the graphing utility to find the hourly wage when 9 units are produced per hour. (d) Use the trace feature of the graphing utility to find the number of units produced per hour when your hourly wage is \(\$ 21.35\)
Determine whether the function is even, odd, or neither (a) algebraically, (b) graphically by using a graphing utility to graph the function, and (c) numerically by using the table feature of the graphing utility to compare \(f(x)\) and \(f(-x)\) for several values of \(x\). $$g(x)=x^{3}-5 x$$
Determine whether the function is even, odd, or neither (a) algebraically, (b) graphically by using a graphing utility to graph the function, and (c) numerically by using the table feature of the graphing utility to compare \(f(x)\) and \(f(-x)\) for several values of \(x\). $$f(t)=t^{2}+2 t-3$$
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