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Chapter 8: Problem 5
Determine whether each relation is a function. Give the domain and range for each relation. $$\\{(-3,-3),(-2,-2),(-1,-1),(0,0)\\}$$
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Find \(f(g(x))\) and \(g(f(x))\) and determine whether each pair of functions \(f\) and \(g\) are inverses of each other. $$f(x)=5 x-9 \quad \text { and } \quad g(x)=\frac{x+5}{9}$$
The regular price of a computer is \(x\) dollars. Let \(f(x)=x-400\) and \(g(x)=0.75 x\) a. Describe what the functions \(f\) and \(g\) model in terms of the price of the computer. b. Find \((f \circ g)(x)\) and describe what this models in terms of the price of the computer. c. Repeatpart(b) for \((g \circ f)(x)\). d. Which composite function models the greater discount on the computer, \(f \circ g\) or \(g \circ f ?\) Explain. e. Find \(f^{-1}\) and describe what this models in terms of the price of the computer.
If \(f(x)=\frac{4}{x-3},\) why must 3 be excluded from the domain of \(f ?\)
If \(f(x)=3 x\) and \(g(x)=x+5,\) find \((f \circ g)^{-1}(x)\) and \(\left(g^{-1} \circ f^{-1}\right)(x)\).
\(f\) and \(g\) are defined by the following tables. Use the tables to evaluate each composite function. $$\begin{array}{c|c}\hline x & f(x) \\\\\hline-1 & 1 \\\\\hline 0 & 4 \\\\\hline 1 & 5 \\\\\hline 2 & -1 \\ \hline\end{array}$$ $$\begin{array}{c|c}\hline x & g(x) \\\\\hline-1 & 0 \\\\\hline 1 & 1 \\\\\hline 4 & 2 \\\\\hline 10 & -1 \\ \hline\end{array}$$ $$(g \circ f)(0)$$
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