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Chapter 8: Problem 29
Find \(f(-x)-f(x)\) for the given function \(f\) Then simplify the expression. $$f(x)=x^{3}+x-5$$
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Use a graphing utility to graph \(f\) and \(g\) in the same viewing rectangle. In addition, graph the line \(y=x\) and visually determine if \(f\) and g are inverses. $$f(x)=4 x+4, \quad g(x)=0.25 x-1$$
Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. If \(\left(\frac{f}{g}\right)(a)=0,\) then \(f(a)\) must be 0
Find \(f(g(x))\) and \(g(f(x))\) and determine whether each pair of functions \(f\) and \(g\) are inverses of each other. $$f(x)=-x \text { and } g(x)=x$$
\(f\) and \(g\) are defined by the following tables. Use the tables to evaluate each composite function. $$\begin{array}{c|c}\hline x & f(x) \\\\\hline-1 & 1 \\\\\hline 0 & 4 \\\\\hline 1 & 5 \\\\\hline 2 & -1 \\ \hline\end{array}$$ $$\begin{array}{c|c}\hline x & g(x) \\\\\hline-1 & 0 \\\\\hline 1 & 1 \\\\\hline 4 & 2 \\\\\hline 10 & -1 \\ \hline\end{array}$$ $$f(g(1))$$
Find \(f(g(x))\) and \(g(f(x))\) and determine whether each pair of functions \(f\) and \(g\) are inverses of each other. $$f(x)=5 x-9 \quad \text { and } \quad g(x)=\frac{x+5}{9}$$
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