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Solutions Homework 7

# Solutions Homework 7 - MATH 106 CALCULUS I FOR BIO SOC SCI...

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MATH 106 CALCULUS I FOR BIO. & SOC. SCI. FALL 2011 INSTRUCTOR: JOS ´ E MANUEL G ´ OMEZ Solutions Homework 7. Please show all your work. (1) (5 Points) Suppose that f and g are differentiable functions such that f (1) = 2 ,f (2) = 1 ,f (1) = 2 ,f (2) = 1 g (1) = 2 ,g (2) = 2 ,g (1) = 3 ,g (2) = 1 . (a) (1 Points) If a ( x ) = f 1 ( x ) compute a (2). Solution: a ( x ) = 1 f ( f 1 ( x )) . Note that f 1 (2) = 1 since f (1) = 2. Therefore a (2) = 1 f ( f 1 (2)) = 1 f (1) = 1 2 . (b) (2 Points) If b ( x ) = f 1 ( x ) compute b (4). Solution: b ( x ) = 1 f ( f 1 ( x )) parenleftbigg 1 2 x 1 / 2 parenrightbigg = 1 f ( f 1 ( x )) parenleftbigg 1 2 x parenrightbigg . Thus b (4) = 1 f ( f 1 ( 4)) parenleftbigg 1 2 4 parenrightbigg = 1 f ( f 1 (2)) parenleftbigg 1 4 parenrightbigg = 1 f (1) parenleftbigg 1 4 parenrightbigg = 1 8 . (c) (1 Points) If c ( x ) = f g 1 ( x ) compute c (2). Solution: c ( x ) = f ( g 1 ( x )) parenleftbigg 1 g ( g 1 ( x )) parenrightbigg Note that g (2) = 2 and thus g 1 (2) = 2. Thus c (2) = f ( g 1 (2)) parenleftbigg 1 g ( g 1 (2)) parenrightbigg = f (2) parenleftbigg 1 g (2) parenrightbigg = 1 .

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Solutions Homework 7 - MATH 106 CALCULUS I FOR BIO SOC SCI...

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