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Chapter 8: Problem 7
Determine whether each relation is a function. Give the domain and range for each relation. $$\\{(1,4),(1,5),(1,6)\\}$$
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Use a graphing utility to graph each function. Use the graph to determine whether the function has an inverse that is a function (that is, whether the function is one-to-one). $$f(x)=(x-1)^{3}$$
\(f\) and \(g\) are defined by the following tables. Use the tables to evaluate each composite function. $$\begin{array}{c|c}\hline x & f(x) \\\\\hline-1 & 1 \\\\\hline 0 & 4 \\\\\hline 1 & 5 \\\\\hline 2 & -1 \\ \hline\end{array}$$ $$\begin{array}{c|c}\hline x & g(x) \\\\\hline-1 & 0 \\\\\hline 1 & 1 \\\\\hline 4 & 2 \\\\\hline 10 & -1 \\ \hline\end{array}$$ $$(g \circ f)(-1)$$
Let \(f(x)=3 x-4\) and \(g(x)=x^{2}+6\) a. Find \(f(5)\) b. Find \(g(f(5))\)
Find \(f(g(x))\) and \(g(f(x))\) and determine whether each pair of functions \(f\) and \(g\) are inverses of each other. $$f(x)=4 x \quad \text { and } \quad g(x)=\frac{x}{4}$$
The functions are all one-to-one. For each function, a. Find an equation for \(f^{-1}(x),\) the inverse function. b. Verify that your equation is correct by showing that \(f\left(f^{-1}(x)\right)=x\) and \(f^{-1}(f(x))=x\). $$f(x)=x+3$$
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