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Question 256549: Can you please do a step by step informative answer for the following question? I am having to take a placement test and cannot for the life of me remember how to perform a function!!! Thanks!
The whole question goes as follows:
Listed below are 5 functions< each denoted g(x) and each involving a real number constant c>1.
If f(x)=2 to the x, which of these 5 functions yeilds the greatest value for
f(g(x)), for all x>1?
a. g(x)=cx
b. g(x)=c/x
c. g(x)=x/c
d. g(x)=x-c
e. g(x)=logsubscriptc x
HELP!
Answer by drk(1908)   (Show Source):
You can put this solution on YOUR website! (a) f(g(x)) will become 2^cx. As x increases f(g(x)) increases
(b) f(g(x)) will become 2^c/x. As x increases f(g(x)) decreases
(c) f(g(x)) will become 2^x/c. As x increases f(g(x)) increases
(d) f(g(x)) will become 2^(x-c). As x increases f(g(x)) increases
(e) f(g(x)) will become 2^(log_c(x)). As x increases f(g(x)) increases
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Now (b) decreases, so it is out of contention.
Since c is a constant, let c = 3. We get
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(a) f(g(x)) will become 2^(3x). As x increases f(g(x)) increases
(c) f(g(x)) will become 2^(x/3). As x increases f(g(x)) increases
(d) f(g(x)) will become 2^(x-3). As x increases f(g(x)) increases
(e) f(g(x)) will become 2^(log_c(x)). As x increases f(g(x)) increases
Now, (c) < (a), so (c) is out. (d) < (a) so (d) is out. We now have:
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(a) f(g(x)) will become 2^(3x). As x increases f(g(x)) increases
(e) f(g(x)) will become 2^(log_c(x)). As x increases f(g(x)) increases
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It turns out that (a) grows a lot faster than (e) so (a) is the largest value.
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