anonymous
  • anonymous
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
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
did you pick two functions?
anonymous
  • anonymous
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
anonymous
  • anonymous
once you have them we can do this easy

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More answers

anonymous
  • anonymous
f(x)= x+7 and g(x)= 1/x+7 were the functions I thought to use for this.
anonymous
  • anonymous
\[f(x)=x+7,g(x)=\frac{1}{x+7}\] like that?
anonymous
  • anonymous
or was \(g(x)=\frac{1}{x}+7\) either way we can do it
anonymous
  • anonymous
you pick
anonymous
  • anonymous
the second one was how I meant to put the second function. sorry ^.^"
anonymous
  • anonymous
ok brave to use a denominator but no problem lets compute \[f(g(x))\] first
anonymous
  • anonymous
always work from the inside out \[f(g(x))=f(\frac{1}{x}+7)\] is a fist step
anonymous
  • anonymous
then since \(f9\heartsuit)=\heartsuit +7\) you have ' \[f(\frac{1}{x}+7)=\frac{1}{x}+7+7\] or more simply \[\frac{1}{x}+14\]
anonymous
  • anonymous
\[f(x)=x+7\] and \[g(x)= \frac{ 1}{ x } +7\] this is how they should look
anonymous
  • anonymous
yeah got it
anonymous
  • anonymous
that makes \[f(g(x))=f(\frac{1}{x}+7)=\frac{1}{x}+7+7=\frac{1}{x}+14\]
anonymous
  • anonymous
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...
anonymous
  • anonymous
yeah for me too
anonymous
  • anonymous
did you see the last one?
anonymous
  • anonymous
Yes! And thank you for your help! I really do appreciate it :3
anonymous
  • anonymous
for the next one it is a bit tricker
anonymous
  • anonymous
\[g(f(x))=g(x+7)=\frac{1}{x+7}+7\]
anonymous
  • anonymous
you can replace \(x\) by 10 in both of those for \[g(f(10))\] you will get \[\frac{1}{10+7}=7=\frac{1}{17}+7=7\tfrac{1}{17}\]
anonymous
  • anonymous
you mean to get the result for Which composite function has the greatest value for x=10?
anonymous
  • anonymous
right
anonymous
  • anonymous
Sorry >.< late response again. But I believe I understand the material. ^w^
anonymous
  • anonymous
ok good stay cool
anonymous
  • anonymous
You too! ^w^ Thanks for the help @satellite73 :3

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