Respuesta :

According to defintion of compostion of functions, we can get:

[tex](f\circ g)(x)=f(g(x))[/tex]

But we know, that:

[tex]\displaystyle h(x)= \frac{x^2}{x^2+4} [/tex]

Our goal, is to express that function as a composition:

[tex](f\circ g)(x)=h(x) \Rightarrow f(g(x))=h(x) [/tex]

I.e:

[tex]\displaystyle f(g(x))=\frac{x^2}{x^2+4}[/tex]

If [tex]\displaystyle f(y)= \frac{y}{y+4} [/tex] then [tex]g(x)=x^2[/tex]. Hence, [tex]\displaystyle h(x)=(f\circ g)(x)=f(g(x))= \frac{g(x)}{g(x)+4} \Rightarrow f(g(x))=f(x^2)= \frac{x^2}{x^2+4} [/tex]

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