SOLUTION: Listed below are 5 functions each denoted g(x) and each involving a real number x constant c>1. If f(x)=2 , which of these 5 functions yeilds the greates

Question 201539: Listed below are 5 functions each denoted g(x) and each involving a real number
x
constant c>1. If f(x)=2 , 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)= log x
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
means this function will take whatever you give it and raise 2 to that power. So when we give it g(x) it will raise 2 to that power:

So now we can see what will happen to this for the various definitions of g(x).
A. g(x)= cx

B. g(x)= c/x

C. g(x)= x/c

D. g(x)= x-c

E. g(x)= log x

Now we just need to figure out which exponent is largest
When c>1 and x>1 ...
A. cx > x and cx > c
B. 1/x is between 0 and 1 so c*(1/x) < c.
C. 1/c is between 0 and 1 so x*(1/c) < x.
D. x-c < x
E. log(x) < x. This is the trickiest one to explain. If you look at graphs of y=x and y=log(x) superimposed on each other you will see that for all x-values the graph of graph of y=log(x) is below the graph of y=x. So log(x) < x for all x. (Unfortunately I can't get Algebra.com software to graph log(x). If I could I'd show you these graphs here.)

In summary, when c>1 and x>1 only c*x is guaranteed to be larger than both c and x. So c*x is the largest exponent which means is the largest which means the answer is A.
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