anonymous
  • anonymous
Express the following function, F(x) as a composition of two functions f and g. f(x)= x^2/(x^2+4) @misty1212
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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misty1212
  • misty1212
you have many choices here, but the easiest one is probably \(g(x)=x^2\) and \(f(x)=\frac{x}{x+4}\)
misty1212
  • misty1212
then if you compose them you get \[f(g(x))=f(x^2)=\frac{x^2}{x^2+4}\]
anonymous
  • anonymous
wait can you show me how you got that?

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misty1212
  • misty1212
how i got which part?
anonymous
  • anonymous
the answer
misty1212
  • misty1212
\[f(g(x))=f(x^2)=\frac{x^2}{x^2+4}\] this?
anonymous
  • anonymous
yes
misty1212
  • misty1212
that is how you compose functions if \(g(x)=x^2\) then \[f(g(x))=f(x^2)\]
misty1212
  • misty1212
this is kind of a crappy explanation, lets see if i can do better
anonymous
  • anonymous
I'm a bit confused....which is the answer?
misty1212
  • misty1212
\[f(g(x))=\frac{x^2}{x^2+4}\] is the question your job is to come up with an \(f\) and a \(g\) that work
misty1212
  • misty1212
when you see \(\frac{x^2}{x^2+4}\) the first thing you notice is that the variable is squared top and bottom right?
anonymous
  • anonymous
right
misty1212
  • misty1212
that is why i picked the "inside function " \(g(x)\) as \(g(x)=x^2\)
misty1212
  • misty1212
then the outside part, since we already know the variable is going to be square, looks something like \[f(\spadesuit)=\frac{\spadesuit}{\spadesuit+4}\]
misty1212
  • misty1212
if you replace \(\spadesuit\) by \(x^2\) you get what you want\[\frac{x^2}{x^2+4}\]
misty1212
  • misty1212
so make the inside function \(g(x)=x^2\) and the outside function \(f(x)=\frac{x}{x+4}\) that way you get what you want when you compose them

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