{"id":1047,"date":"2015-11-12T18:35:32","date_gmt":"2015-11-12T18:35:32","guid":{"rendered":"https:\/\/courses.candelalearning.com\/collegealgebra1xmaster\/?post_type=chapter&p=1047"},"modified":"2015-11-12T18:35:32","modified_gmt":"2015-11-12T18:35:32","slug":"solutions-50","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/chapter\/solutions-50\/","title":{"raw":"Solutions","rendered":"Solutions"},"content":{"raw":"

Solutions to Try Its<\/h2>\n1.\u00a0[latex]h\\left(2\\right)=6[\/latex]\n\n2.\u00a0Yes\n\n3.\u00a0Yes\n\n4.\u00a0The domain of function [latex]{f}^{-1}[\/latex] is [latex]\\left(-\\infty \\text{,}-2\\right)[\/latex] and the range of function [latex]{f}^{-1}[\/latex] is [latex]\\left(1,\\infty \\right)[\/latex].\n\n5. a.\u00a0[latex]f\\left(60\\right)=50[\/latex]. In 60 minutes, 50 miles are traveled.\n\nb. [latex]{f}^{-1}\\left(60\\right)=70[\/latex]. To travel 60 miles, it will take 70 minutes.\n\n6.\u00a0a. 3; b. 5.6\n\n7.\u00a0[latex]x=3y+5[\/latex]\n\n8.\u00a0[latex]{f}^{-1}\\left(x\\right)={\\left(2-x\\right)}^{2};\\text{domain}\\text{of}f:\\left[0,\\infty \\right);\\text{domain}\\text{of}{f}^{-1}:\\left(-\\infty ,2\\right]\\\\[\/latex]\n\n9.\n\"Graph

Solutions to Odd-Numbered Exercises<\/h2>\n1.\u00a0Each output of a function must have exactly one output for the function to be one-to-one. If any horizontal line crosses the graph of a function more than once, that means that [latex]y[\/latex] -values repeat and the function is not one-to-one. If no horizontal line crosses the graph of the function more than once, then no [latex]y[\/latex] -values repeat and the function is one-to-one.\n\n3.\u00a0Yes. For example, [latex]f\\left(x\\right)=\\frac{1}{x}\\\\[\/latex] is its own inverse.\n\n5.\u00a0Given a function [latex]y=f\\left(x\\right)[\/latex], solve for [latex]x[\/latex] in terms of [latex]y[\/latex]. Interchange the [latex]x[\/latex] and [latex]y[\/latex]. Solve the new equation for [latex]y[\/latex]. The expression for [latex]y[\/latex] is the inverse, [latex]y={f}^{-1}\\left(x\\right)[\/latex].\n\n7.\u00a0[latex]{f}^{-1}\\left(x\\right)=x - 3[\/latex]\n\n9.\u00a0[latex]{f}^{-1}\\left(x\\right)=2-x[\/latex]\n\n11.\u00a0[latex]{f}^{-1}\\left(x\\right)=\\frac{-2x}{x - 1}\\\\[\/latex]\n\n13.\u00a0domain of [latex]f\\left(x\\right):\\left[-7,\\infty \\right);{f}^{-1}\\left(x\\right)=\\sqrt{x}-7[\/latex]\n\n15.\u00a0domain of [latex]f\\left(x\\right):\\left[0,\\infty \\right);{f}^{-1}\\left(x\\right)=\\sqrt{x+5}\\\\[\/latex]\n\n17.\u00a0[latex] f\\left(g\\left(x\\right)\\right)=x,g\\left(f\\left(x\\right)\\right)=x[\/latex]\n\n19. one-to-one\n\n21.\u00a0one-to-one\n\n23.\u00a0not one-to-one\n\n25.\u00a0[latex]3[\/latex]\n\n27.\u00a0[latex]2[\/latex]\n\n29.\n\"Graph\n\n31.\u00a0[latex]\\left[2,10\\right][\/latex]\n\n33.\u00a0[latex]6[\/latex]\n\n35.\u00a0[latex]-4[\/latex]\n\n37.\u00a0[latex]0[\/latex]\n\n39.\u00a0[latex]1[\/latex]\n\n41.\n
[latex]x[\/latex]<\/td>\n1<\/td>\n4<\/td>\n7<\/td>\n12<\/td>\n16<\/td>\n<\/tr>
[latex]{f}^{-1}\\left(x\\right)\\\\[\/latex]<\/td>\n3<\/td>\n6<\/td>\n9<\/td>\n13<\/td>\n14<\/td>\n<\/tr><\/tbody><\/table>\n43. [latex]{f}^{-1}\\left(x\\right)={\\left(1+x\\right)}^{1\/3}\\\\[\/latex]\n\"Graph\n\n45.\u00a0[latex]{f}^{-1}\\left(x\\right)=\\frac{5}{9}\\left(x - 32\\right)\\\\[\/latex]. Given the Fahrenheit temperature, [latex]x[\/latex], this formula allows you to calculate the Celsius temperature.\n\n47.\u00a0[latex]t\\left(d\\right)=\\frac{d}{50}\\\\[\/latex], [latex]t\\left(180\\right)=\\frac{180}{50}\\\\[\/latex]. The time for the car to travel 180 miles is 3.6 hours.","rendered":"

Solutions to Try Its<\/h2>\n

1.\u00a0[latex]h\\left(2\\right)=6[\/latex]<\/p>\n

2.\u00a0Yes<\/p>\n

3.\u00a0Yes<\/p>\n

4.\u00a0The domain of function [latex]{f}^{-1}[\/latex] is [latex]\\left(-\\infty \\text{,}-2\\right)[\/latex] and the range of function [latex]{f}^{-1}[\/latex] is [latex]\\left(1,\\infty \\right)[\/latex].<\/p>\n

5. a.\u00a0[latex]f\\left(60\\right)=50[\/latex]. In 60 minutes, 50 miles are traveled.<\/p>\n

b. [latex]{f}^{-1}\\left(60\\right)=70[\/latex]. To travel 60 miles, it will take 70 minutes.<\/p>\n

6.\u00a0a. 3; b. 5.6<\/p>\n

7.\u00a0[latex]x=3y+5[\/latex]<\/p>\n

8.\u00a0[latex]{f}^{-1}\\left(x\\right)={\\left(2-x\\right)}^{2};\\text{domain}\\text{of}f:\\left[0,\\infty \\right);\\text{domain}\\text{of}{f}^{-1}:\\left(-\\infty ,2\\right]\\\\[\/latex]<\/p>\n

9.
\n\"Graph<\/p>\n

Solutions to Odd-Numbered Exercises<\/h2>\n

1.\u00a0Each output of a function must have exactly one output for the function to be one-to-one. If any horizontal line crosses the graph of a function more than once, that means that [latex]y[\/latex] -values repeat and the function is not one-to-one. If no horizontal line crosses the graph of the function more than once, then no [latex]y[\/latex] -values repeat and the function is one-to-one.<\/p>\n

3.\u00a0Yes. For example, [latex]f\\left(x\\right)=\\frac{1}{x}\\\\[\/latex] is its own inverse.<\/p>\n

5.\u00a0Given a function [latex]y=f\\left(x\\right)[\/latex], solve for [latex]x[\/latex] in terms of [latex]y[\/latex]. Interchange the [latex]x[\/latex] and [latex]y[\/latex]. Solve the new equation for [latex]y[\/latex]. The expression for [latex]y[\/latex] is the inverse, [latex]y={f}^{-1}\\left(x\\right)[\/latex].<\/p>\n

7.\u00a0[latex]{f}^{-1}\\left(x\\right)=x - 3[\/latex]<\/p>\n

9.\u00a0[latex]{f}^{-1}\\left(x\\right)=2-x[\/latex]<\/p>\n

11.\u00a0[latex]{f}^{-1}\\left(x\\right)=\\frac{-2x}{x - 1}\\\\[\/latex]<\/p>\n

13.\u00a0domain of [latex]f\\left(x\\right):\\left[-7,\\infty \\right);{f}^{-1}\\left(x\\right)=\\sqrt{x}-7[\/latex]<\/p>\n

15.\u00a0domain of [latex]f\\left(x\\right):\\left[0,\\infty \\right);{f}^{-1}\\left(x\\right)=\\sqrt{x+5}\\\\[\/latex]<\/p>\n

17.\u00a0[latex]f\\left(g\\left(x\\right)\\right)=x,g\\left(f\\left(x\\right)\\right)=x[\/latex]<\/p>\n

19. one-to-one<\/p>\n

21.\u00a0one-to-one<\/p>\n

23.\u00a0not one-to-one<\/p>\n

25.\u00a0[latex]3[\/latex]<\/p>\n

27.\u00a0[latex]2[\/latex]<\/p>\n

29.
\n\"Graph<\/p>\n

31.\u00a0[latex]\\left[2,10\\right][\/latex]<\/p>\n

33.\u00a0[latex]6[\/latex]<\/p>\n

35.\u00a0[latex]-4[\/latex]<\/p>\n

37.\u00a0[latex]0[\/latex]<\/p>\n

39.\u00a0[latex]1[\/latex]<\/p>\n

41.<\/p>\n\n\n\n\n
[latex]x[\/latex]<\/td>\n1<\/td>\n4<\/td>\n7<\/td>\n12<\/td>\n16<\/td>\n<\/tr>\n
[latex]{f}^{-1}\\left(x\\right)\\\\[\/latex]<\/td>\n3<\/td>\n6<\/td>\n9<\/td>\n13<\/td>\n14<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

43. [latex]{f}^{-1}\\left(x\\right)={\\left(1+x\\right)}^{1\/3}\\\\[\/latex]
\n\"Graph<\/p>\n

45.\u00a0[latex]{f}^{-1}\\left(x\\right)=\\frac{5}{9}\\left(x - 32\\right)\\\\[\/latex]. Given the Fahrenheit temperature, [latex]x[\/latex], this formula allows you to calculate the Celsius temperature.<\/p>\n

47.\u00a0[latex]t\\left(d\\right)=\\frac{d}{50}\\\\[\/latex], [latex]t\\left(180\\right)=\\frac{180}{50}\\\\[\/latex]. The time for the car to travel 180 miles is 3.6 hours.<\/p>\n\n\t\t\t

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