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Chapter 1: Problem 16
Find the domain of each function. $$f(x)=\frac{1}{\frac{4}{x-2}-3}$$
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I graphed $$f(x)=\left\\{\begin{array}{lll} 2 & \text { if } & x \neq 4 \\ 3 & \text { if } & x=4 \end{array}\right.$$ and one piece of my graph is a single point.
Will help you prepare for the material covered in the next section. Find the perimeter and the area of each rectangle with the given dimensions: a. 40 yards by 30 yards b. 50 yards by 20 yards.
Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. $$x^{2}+y^{2}-6 y-7=0$$
Use a graphing utility to graph each function. Use \(a[-5,5,1]\) by [-5,5,1] viewing rectangle. Then find the intervals on which the function is increasing, decreasing, or constant. $$h(x)=2-x^{\frac{2}{5}}$$
114\. If \(f(x)=x^{2}-4\) and \(g(x)=\sqrt{x^{2}-4},\) then \((f \circ g)(x)=-x^{2}\) and \(\left(f^{\circ} g\right)(5)=-25\) 115\. There can never be two functions \(f\) and \(g\), where \(f \neq g\), for which \((f \circ g)(x)=(g \circ f)(x)\) 116\. If \(f(7)=5\) and \(g(4)=7,\) then \((f \circ g)(4)=35\) 117\. If \(f(x)=\sqrt{x}\) and \(g(x)=2 x-1,\) then \((f \circ g)(5)=g(2)\) 118\. Prove that if \(f\) and \(g\) are even functions, then \(f g\) is also an even function. 119\. Define two functions \(f\) and \(g\) so that \(f^{\circ} g=g \circ f\)
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