SOLUTION: 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 yie

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
======================================
Cheers,
Stan H.

RELATED QUESTIONS
Listed below are 5 functions each denoted g(x) and each involving a real number (answered by jsmallt9)

Listed below are 5 functions each denoted g(x) and each involving a real number x... (answered by jim_thompson5910)

Can you please do a step by step informative answer for the following question? I am... (answered by drk)

Listed below are 5 functions, each denoted g(x) and each involving a real number constant (answered by stanbon)

Let g and f be two functions defined by g(x)=(-5+x)(2+x) f(x)=2-9x for any real... (answered by ReadingBoosters)

Without graphing, answer the following questions for each of the functions below: i.... (answered by solver91311)

CAN SOMEONE PLEASE HELP ME WITH THIS PROBLEM: If f(g(x)) = g(f(x)) = x, then whay can... (answered by jim_thompson5910)

CAN SOMEONE PLEASE HELP ME WITH THIS PROBLEM: If f(g(x)) = g(f(x)) = x, then what can... (answered by stanbon)

Im stuck on this problem. Please help me by showing all the steps and equation. Thank... (answered by vleith)