Question

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

Answer 1

you have many choices here, but the easiest one is probably \(g(x)=x^2\) and \(f(x)=\frac{x}{x+4}\)

Answer 2

then if you compose them you get \[f(g(x))=f(x^2)=\frac{x^2}{x^2+4}\]

Answer 3

wait can you show me how you got that?

Answer 4

how i got which part?

Answer 5

the answer

Answer 6

\[f(g(x))=f(x^2)=\frac{x^2}{x^2+4}\] this?

Answer 7

yes

Answer 8

that is how you compose functions
if \(g(x)=x^2\) then \[f(g(x))=f(x^2)\]

Answer 9

this is kind of a crappy explanation, lets see if i can do better

Answer 10

I'm a bit confused....which is the answer?

Answer 11

\[f(g(x))=\frac{x^2}{x^2+4}\] is the question
your job is to come up with an \(f\) and a \(g\) that work

Answer 12

when you see \(\frac{x^2}{x^2+4}\) the first thing you notice is that the variable is squared top and bottom right?

Answer 13

right

Answer 14

that is why i picked the "inside function " \(g(x)\) as \(g(x)=x^2\)

Answer 15

then the outside part, since we already know the variable is going to be square, looks something like
\[f(\spadesuit)=\frac{\spadesuit}{\spadesuit+4}\]

Answer 16

if you replace \(\spadesuit\) by \(x^2\) you get what you want\[\frac{x^2}{x^2+4}\]

Answer 17

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