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Chapter 2: Problem 1
Find \(f(g(x))\) and \(g(f(x))\) and determine whether each pair of functions \(f\) and \(g\) are inverses of each other. $$f(x)=4 x \text { and } g(x)=\frac{x}{4}$$
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Begin by graphing the absolute value function, \(f(x)=|x| .\) Then use transformations of this graph to graph the given function. $$ g(x)=|x+4| $$
Assume that \((a, b)\) is a point on the graph of \(f .\) What is the corresponding point on the graph of each of the following functions? $$ y=f(x-3) $$
Begin by graphing the square root function, \(f(x)=\sqrt{x} .\) Then use transformations of this graph to graph the given function. $$ g(x)=\sqrt{x}+1 $$
A formula in the form \(y=m x+b\) models the cost, \(y,\) of a four-year college \(x\) years after \(2003 .\) Would you expect \(m\) to be positive, negative, or zero? Explain your answer.
Begin by graphing the square root function, \(f(x)=\sqrt{x} .\) Then use transformations of this graph to graph the given function. $$ g(x)=\sqrt{x+1} $$
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