WILL BECOME FAN AND AWARD MEDAL!!! Make up any two functions f(x) and g(x), defined in terms of the variable x. For example, you might define f(x) = x – 15 and g(x) = 3x2. (Use different examples.) Then provide the compositions of the two functions f(g(x)) and g(f(x)). Which composite function has the greatest value for x = 10? Remember no right answer exists. Your answer completely depends on the functions you select.

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WILL BECOME FAN AND AWARD MEDAL!!! Make up any two functions f(x) and g(x), defined in terms of the variable x. For example, you might define f(x) = x – 15 and g(x) = 3x2. (Use different examples.) Then provide the compositions of the two functions f(g(x)) and g(f(x)). Which composite function has the greatest value for x = 10? Remember no right answer exists. Your answer completely depends on the functions you select.

Mathematics
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did you pick two functions?
go ahead and make two up they can be anything, but you don't want to make them too hard, so stick with something simple
once you have them we can do this easy

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Other answers:

f(x)= x+7 and g(x)= 1/x+7 were the functions I thought to use for this.
\[f(x)=x+7,g(x)=\frac{1}{x+7}\] like that?
or was \(g(x)=\frac{1}{x}+7\) either way we can do it
you pick
the second one was how I meant to put the second function. sorry ^.^"
ok brave to use a denominator but no problem lets compute \[f(g(x))\] first
always work from the inside out \[f(g(x))=f(\frac{1}{x}+7)\] is a fist step
then since \(f9\heartsuit)=\heartsuit +7\) you have ' \[f(\frac{1}{x}+7)=\frac{1}{x}+7+7\] or more simply \[\frac{1}{x}+14\]
\[f(x)=x+7\] and \[g(x)= \frac{ 1}{ x } +7\] this is how they should look
yeah got it
that makes \[f(g(x))=f(\frac{1}{x}+7)=\frac{1}{x}+7+7=\frac{1}{x}+14\]
Sorry. My computer is messing up so I'm having a hard time seeing your responses. I'm not sure why open study isn't working properly for me, but it isn't...
yeah for me too
did you see the last one?
Yes! And thank you for your help! I really do appreciate it :3
for the next one it is a bit tricker
\[g(f(x))=g(x+7)=\frac{1}{x+7}+7\]
you can replace \(x\) by 10 in both of those for \[g(f(10))\] you will get \[\frac{1}{10+7}=7=\frac{1}{17}+7=7\tfrac{1}{17}\]
you mean to get the result for Which composite function has the greatest value for x=10?
right
Sorry >.< late response again. But I believe I understand the material. ^w^
ok good stay cool
You too! ^w^ Thanks for the help @satellite73 :3

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