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Unformatted text preview: MAC1147: Quiz #5
09/29/2009
In the topright 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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 Summer '08
 GERMAN
 Calculus, 60%, 90%, 1800 k

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