quiz5solutions - MAC1147 Quiz#5 In the top-right corner of...

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Unformatted text preview: MAC1147: Quiz #5 09/29/2009 In the top-right corner of a clean sheet of paper, write your name, UFID, and section number. Please use a pen with blue or black ink. When you are nished, FOLD your paper in half lengthwise and write your name on the back. √ 1 and g (x) = x. Find f (g (x)) and state its domain. x−1 √ 1 f (g (x)) = f ( x) = √ . To nd the domain of f (g (x)), we must x−2 √ take the intersection of the domain of g (x) = x, which is [0, ∞), with 1 , which is x = 4. So the domain of g (f (x)) is the domain of √ x−2 [0, 4) ∪ (4, ∞). 1. Let f (x) = x−1 . Use f −1 (x) to nd the range of f . x+2 y−1 x−1 f (x) = y = ⇒x= ⇒ x(y +2) = y −1 ⇒ xy +2x = y −1 ⇒ x+2 y+2 −2x − 1 xy − y = −2x − 1 ⇒ y (x − 1) = −2x − 1 ⇒ y = f −1 (x) = . The x−1 range of f (x) is simply the domain of f −1 (x), which is (−∞, 1) ∪ (1, ∞). 2. Let f (x) = 3. The grade a student receives on an exam varies inversely with the number of hours per week spent on Facebook. If a student who spends 20 hours per week on Facebook earned a 60% on the exam, how many hours were spent on Facebook by a student who earned a 90%? k The inverse proportionality gives that y = , where y is the exam x grade and x is hours spent on Facebook. The 2nd sentence gives the 1 relation 60 = 1800 k ⇒ k = 1800. We then have 90 = ⇒ x = 20. 20 x 2 ...
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quiz5solutions - MAC1147 Quiz#5 In the top-right corner of...

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