Math_137_Winter_2010_Solution_1

# Math_137_Winter_2010_Solution_1 - Math 137 Winter 2010...

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Math 137 Winter 2010 Assignment 1 Due Friday, January 15 Text problems: Section 1.1: 30. Find the domain of the function. 40. Find the domain of the function and sketch the graph of the function. 64. Complete the graph of f if it is know that f is a) even b) odd. Section 1.3:

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6. Use transformations on function f(x) to create the graph shown. 3x-6-(x 2 -4x+4) -x 2 +7x-10 20. Graph the function by means of basic transformations. 28. Use the given graph of f to sketch the graph of y = 1/f(x). Which features of f are the most important in sketching y? Explain how they are used. 34. Let f(x) = x and 3 1 ) ( x x g = . Find f ° g, g ° f, f ° f and g ° g and their domains. Dom f = {x | x 0} and Dom g = . a) 6 3 3 1 1 ) 1 ( )) ( ( x x x f x g f = = = Dom f ° g = {x | x 1} b) 3 1 ) ( )) ( ( x x g x f g = =
Dom g ° f = {x | x 0} c) f(f(x)) = f( x) = √√ x = 4 x Dom f ° f = {x | x 0} d) 3 3 3 1 1 ) 1 ( )) ( ( x x g x g g = = Dom g ° g = Appendix A: 30. Solve x 2 + x > 1 and show the solution on the real number line. We will subtract 1 from both sides of the inequality, and factor: 0 ) 2 5 1 )( 2 5 1 ( 1 2 > + + + = + x x x x . This statement is true if either both factors are positive, or both are negative. Hence the solution set is (– , (–1 – 5)/2) ((–1 + 5)/2, ) 46. Solve | 2x – 1 | / | x + 1 | = 3 Note that | x + 1| 0, so x – 1. Since | x + 1 | is nonzero, we multiply both sides by | x + 1|:

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Math_137_Winter_2010_Solution_1 - Math 137 Winter 2010...

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