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Pre-Calc Homework Solutions 39

Pre-Calc Homework Solutions 39 - Chapter 1 Review 43(a f...

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43. (a) ( f + g )( x ) 5 f ( g ( x )) 5 f ( ˇ x w 1 w 2 w ) 5 2 2 ( ˇ x w 1 w 2 w ) 2 5 2 x , x \$ 2 2 ( g + f )( x ) 5 g ( f ( x )) 5 g (2 2 x 2 ) 5 ˇ (2 w 2 w x w 2 ) w 1 w 2 w 5 ˇ 4 w 2 w x w 2 w (b) Domain of f + g: [ 2 2, ) Domain of g + f: [ 2 2, 2] (c) Range of f + g: ( 2‘ , 2] Range of g + f: [0, 2] 44. (a) ( f + g )( x ) 5 f ( g ( x )) 5 f ( ˇ 1 w 2 w x w ) 5 ˇ ˇ w 1 w w 2 w w x w w 5 ˇ 4 1 w 2 w x w ( g + f )( x ) 5 g ( f ( x )) 5 g ( ˇ x w ) 5 ˇ 1 w 2 w ˇ w x w w (b) Domain of f + g: ( 2‘ , 1] Domain of g + f: [0, 1] (c) Range of f + g: [0, ) Range of g + f: [0, 1] 45. (a) [ 2 6, 6] by [ 2 4, 4] Initial point: (5, 0) Terminal point: (5, 0) The ellipse is traced exactly once in a counterclockwise direction starting and ending at the point (5, 0). (b) Substituting cos t 5 } 5 x } and sin t 5 } 2 y } in the identity cos 2 t 1 sin 2 t 5 1 gives the Cartesian equation 1 } 5 x } 2 2 1 1 } 2 y } 2 2 5 1. The entire ellipse is traced by the curve. 46. (a) [ 2 9, 9] by [ 2 6, 6] Initial point: (0, 4) Terminal point: None (since the endpoint } 3 2 p } is not included in the t -interval) The semicircle is traced in a counterclockwise direction
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