Pre-Calc Homework Solutions 24

# Pre-Calc Homework Solutions 24 - (1.58 3(b No points of...

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3. continued (c) g + f : [ 2 4.7, 4.7] by [ 2 3.1, 3.1] 4. It appears that ( f + g )( x ) 5 ( g + f )( x ) 5 x , suggesting that f and g may be inverse of each other. (Notice that the domain of f + g is (0, ) and the domain of g + f is ( 2‘ , ).) (a) f and g : [ 2 4.7, 4.7] by [ 2 3.1, 3.1] (b) f + g : [ 2 4.7, 4.7] by [ 2 3.1, 3.1] (c) g + f : [ 2 4.7, 4.7] by [ 2 3.1, 3.1] Exploration 2 Supporting the Product Rule 1. They appear to be vertical translations of each other. [ 2 1, 8] by [ 2 2, 4] 2. This graph suggests that each difference ( y 3 5 y 1 2 y 2 ) is a constant. [ 2 1, 8] by [ 2 2, 4] 3. y 3 5 y 1 2 y 2 5 ln ( ax ) 2 ln x 5 ln a 1 ln x 2 ln x 5 ln a Thus, the difference y 3 5 y 1 2 y 2 is the constant ln a . Quick Review 1.5 1. ( f + g )(1) 5 f ( g (1)) 5 f (2) 5 1 2. ( g + f )( 2 7) 5 g ( f ( 2 7)) 5 g ( 2 2) 5 5 3. ( f + g )( x ) 5 f ( g ( x )) 5 f ( x 2 1 1) 5 ˇ 3 ( x w 2 w 1 w 1 w ) w 2 w 1 w 5 ˇ 3 x 2 w 5 x 2/3 4. ( g + f )( x ) 5 g ( f ( x )) 5 g ( ˇ 3 x w 2 w 1 w ) 5 ( ˇ 3 x w 2 w 1 w ) 2 1 1 5 ( x 2 1) 2/3 1 1 5. Substituting t for x , one possible answer is: x 5 t , y 5 } t 2 1 1 } , t \$ 2. 6. Substituting t for x , one possible answer is: x 5 t , y 5 t , t ,2 3. 7. [ 2 10, 10] by [ 2 10, 10] (4, 5) 8. [ 2 10, 10] by [ 2 10, 10] 1 } 8 3 } , 2 3 2 < (2.67, 2 3) 9. (a) [ 2 10, 10] by [ 2 10, 10]
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Unformatted text preview: (1.58, 3) (b) No points of intersection, since 2 x . 0 for all values of x . 10. (a) [ 2 10, 10] by [ 2 10, 10] ( 2 1.39, 4) (b) No points of intersection, since e 2 x . 0 for all values of x . Section 1.5 Exercises 1. No, since (for example) the horizontal line y 5 2 intersects the graph twice. 2. Yes, since each horizontal line intersects the graph only once. 3. Yes, since each horizontal line intersects the graph at most once. 4. No, since (for example) the horizontal line y 5 0.5 intersects the graph twice. 5. Yes, since each horizontal line intersects the graph only once. 6. No, since (for example) the horizontal line y 5 2 intersects the graph at more than one point. 24 Section 1.5...
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