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Unformatted text preview: Solutions to Quiz 2B
www.math.uﬂ.edu/ harringt
January 17, 2008
1
1. Let f (x) = x . Find f (x)−f (b)
.
x− b Be sure to SIMPLIFY.
−1
b
x−b
b−x
=
xb(x − b)
x−b
=−
xb(x − b)
1
=−
xb f (x) − f (b)
=
x−b 1
x 2. Find ALL values of x in the interval [0, 2π ] that satisfy cos x = cot x.
cos x
sin x
sin x cos x = cos x
sin x cos x − cos x = 0
cos x(sin x − 1) = 0
cos x = Thus, we have either cos x = 0 or sin x = 1.
π
(a) When cos x = 0, we have x = π , 32 in our interval.
2 (b) When sin x = 1, we have x = π
2 in our interval. π
Hence, our solution set is π , 32 . (Did you remember to check to make
2
sure we did not divide by zero?) 3. Determine the validity of the statement.
√
(a) ”The domain of x + 5 is [−5, ∞).”
This statement is TRUE.
1 (b) ”The graph of f (x) + 3 is obtained by shifting f (x) three units to
the left.”
This statement is FALSE. The correct statemtent should read:
”The graph of f (x) + 3 is obtained by shifting f (x) three units
upward.” 2 ...
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