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Chapter 2: Problem 10
Find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimals places. $$(0,-2) \text { and }(4,3)$$
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Exercises \(103-105\) will help you prepare for the material covered in the next section. Use a rectangular coordinate system to graph the circle with center \((1,-1)\) and radius 1.
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. Repeat part (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.
Exercises \(103-105\) will help you prepare for the material covered in the next section. Solve by completing the square: \(y^{2}-6 y-4=0\).
Express the given function \(h\) as \(a\) composition of two functions \(f\) and \(g\) so that \(h(x)=(f \circ g)(x)\). $$h(x)=\frac{1}{4 x+5}$$
Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$ \begin{aligned} &\text { If } f(x)=x^{2}-4 \text { and } g(x)=\sqrt{x^{2}-4}, \text { then }(f \circ g)(x)=-x^{2}\\\ &\text { and }(f \circ g)(5)=-25 \end{aligned} $$
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