## 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

1. misty1212

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

2. misty1212

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

3. anonymous

wait can you show me how you got that?

4. misty1212

how i got which part?

5. anonymous

6. misty1212

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

7. anonymous

yes

8. misty1212

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

9. misty1212

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

10. anonymous

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

11. 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

12. 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?

13. anonymous

right

14. misty1212

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

15. misty1212

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

16. misty1212

if you replace $$\spadesuit$$ by $$x^2$$ you get what you want$\frac{x^2}{x^2+4}$

17. 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