Question 313545: Listed below are 5 functions, each denoted g(x) and each involving a real number constant
c > 1. If f(x) = 2^x, which of these 5 functions yields 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) = logcx (the c is the base the x is not)
I don't understand how to solve this problem. Can someone please explain it to me. Thank you
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Listed below are 5 functions, each denoted g(x) and each involving a real number constant c > 1.
---------------------------------------
If f(x) = 2^x, which of these 5 functions yields the greatest value for
f(g(x)), for all x > 1 ?
A. g(x) = cx
f(g(x)) = f(cx) = 2^(cx)
-------------------------------
B. g(x) = c^x
f(g(x)) = f(c^x) = 2^(c^x)
-------------------------------
C. g(x) = x^c
f(g(x)) = 2^(x^c)
-------------------------------
D. g(x) = x – c
f(g(x)) = 2^(x-c) = 2^x/2^c
----------------------------------
E. g(x) = logcx (the c is the base the x is not)
f(g(x)) = 2^(logc(x))
----------------------------------
I don't understand how to solve this problem. Can someone please explain it to me.
Procedure: Let c = 3 ; then compare the graphs of f(g(x)) for each of
a,b,c,d,e.
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Cheers,
Stan H.
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