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Chapter 2: Problem 3
Find \(f(g(x))\) and \(g(f(x))\) and determine whether each pair of functions \(f\) and \(g\) are inverses of each other. $$ f(x)=3 x+8 \text { and } g(x)=\frac{x-8}{3} $$
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The toll to a bridge costs \(\$ 6.00 .\) Commuters who frequently use the bridge have the option of purchasing a monthly discount pass for \(\$ 30.00 .\) With the discount pass, the toll is reduced to \(\$ 4.00 .\) For how many bridge crossings per month will the cost without the discount pass be the same as the cost with the discount pass? What will be the monthly cost for each option? (Section \(1.3,\) Example 3 )
Use a graphing utility to graph each circle whoseequation is given. Use a square setting for the viewing window. $$x^{2}+10 x+y^{2}-4 y-20=0$$
In your own words, describe how to find the distance between two points in the rectangular coordinate system.
Graph \(y_{1}=x^{2}-2 x, y_{2}=x,\) and \(y_{3}=y_{1} \div y_{2}\) in the same \([-10,10,1]\) by \([-10,10,1]\) viewing rectangle. Then use the TRACE \(]\) feature to trace along \(y_{3} .\) What happens at \(x=0 ?\) Explain why this occurs.
Exercises \(103-105\) will help you prepare for the material covered in the next section. Solve by completing the square: \(y^{2}-6 y-4=0\).
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