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anonymous
 one year ago
Express the following function, F(x) as a composition of two functions f and g.
f(x)= x^2/(x^2+4) @misty1212
anonymous
 one year ago
Express the following function, F(x) as a composition of two functions f and g. f(x)= x^2/(x^2+4) @misty1212

This Question is Closed

misty1212
 one year ago
Best ResponseYou've already chosen the best response.0you have many choices here, but the easiest one is probably \(g(x)=x^2\) and \(f(x)=\frac{x}{x+4}\)

misty1212
 one year ago
Best ResponseYou've already chosen the best response.0then if you compose them you get \[f(g(x))=f(x^2)=\frac{x^2}{x^2+4}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0wait can you show me how you got that?

misty1212
 one year ago
Best ResponseYou've already chosen the best response.0how i got which part?

misty1212
 one year ago
Best ResponseYou've already chosen the best response.0\[f(g(x))=f(x^2)=\frac{x^2}{x^2+4}\] this?

misty1212
 one year ago
Best ResponseYou've already chosen the best response.0that is how you compose functions if \(g(x)=x^2\) then \[f(g(x))=f(x^2)\]

misty1212
 one year ago
Best ResponseYou've already chosen the best response.0this is kind of a crappy explanation, lets see if i can do better

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm a bit confused....which is the answer?

misty1212
 one year ago
Best ResponseYou've already chosen the best response.0\[f(g(x))=\frac{x^2}{x^2+4}\] is the question your job is to come up with an \(f\) and a \(g\) that work

misty1212
 one year ago
Best ResponseYou've already chosen the best response.0when you see \(\frac{x^2}{x^2+4}\) the first thing you notice is that the variable is squared top and bottom right?

misty1212
 one year ago
Best ResponseYou've already chosen the best response.0that is why i picked the "inside function " \(g(x)\) as \(g(x)=x^2\)

misty1212
 one year ago
Best ResponseYou've already chosen the best response.0then the outside part, since we already know the variable is going to be square, looks something like \[f(\spadesuit)=\frac{\spadesuit}{\spadesuit+4}\]

misty1212
 one year ago
Best ResponseYou've already chosen the best response.0if you replace \(\spadesuit\) by \(x^2\) you get what you want\[\frac{x^2}{x^2+4}\]

misty1212
 one year ago
Best ResponseYou've already chosen the best response.0so 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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