evenans36 - Even-Numbered Answers to Exercise Set 3.6:...

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Even-Numbered Answers to Exercise Set 3.6: Combining Functions −6 −4 −2 2 4 6 8 −8 −6 −4 −2 2 4 x y 2. (a) 3 1 4 ) 2 ( ) 2 ( = = g f . (b) 1 3 2 ) 0 ( ) 0 ( = = g f . (c) ) 4 ( ) 4 ( g f is undefined, since ) 4 ( g is undefined. (d) 5 5 0 ) 2 ( ) 2 ( = = g f . (e) 8 6 2 ) 4 ( ) 4 ( = = g f . (f) Graph of g f : (g) The domain of g f is [] 6 , 3 , since this is where the domains of f and g intersect (overlap). 4. (a) 15 3 2 ) )( ( 2 3 + + + = + x x x x g f Domain: () , (b) 15 13 2 ) )( ( 2 3 = x x x x g f Domain: , (c) x x x x x x fg 75 40 25 16 2 ) )( ( 2 3 4 5 + + = Domain: , (d) ) 3 )( 5 ( 5 2 15 8 5 2 ) ( 3 2 3 + + = + + = x x x x x x x x x g f Domain: ), , 3 ( ) 3 , 5 ( 5 , i . e . 3 and 5 x x . 6. (a) 5 2 4 ) )( ( + = + x x x g f Domain: ), , 5 ( 5 , i . e . 5 x . (b) 5 2 4 ) )( ( = x x x g f Domain: ), , 5 ( 5 , i . e . 5 x . (c) 2 ) 5 ( 8 ) )( ( = x x x fg Domain: ( ) ), , 5 ( 5 , i . e .
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evenans36 - Even-Numbered Answers to Exercise Set 3.6:...

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