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Question 256093: Please help me with this.
Listed below are 5 functions, each denoted g(x) and each involving a real number constant c>1. If f(x)=2x ( 2 exponent x), which of these 5 functions yields the greatest value for f(g(x)), for all x>1?
g(x)=cx
g(x)=c/x
g(x)=x/c
g(x)=x-c
g(x)=logcx
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 ( 2 exponent x), which of these 5 functions yields the greatest value for f(g(x)), for all x>1?
g(x)=cx
f[g(x)] = f[cx] = 2^(cx)
goes to infinity as x gets larger
------------------------
g(x)=c/x
f[g(x)] = f[c/x] = 2^(c/x)
goes to 1 as x gets larger
-------------------------
g(x)=x/c
f[g(x)} = 2^(x/c)
goes to infinity as x gets larger
--------------------------
g(x)=x-c
f[g(x)] = 2^(x-c)
Goes to infinity as x gets larger
------------------------
g(x)=logcx
f[g(x)] = 2^(log(cx)]
goes to infinity as x gets larger
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Cheers,
Stan H.
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