Question

Express the following function, F(x), as a composition of two functions, f and g. f(g(x)).

F(x)= x^2/(x^2+4)

Verify that f(g(x)) = F(x)

Answer 1

Consider $F(x)=(f \circ g)(x)$

Composition of function is the function of a function

Therefore, $F(x)=f(g(x))$

$F(x)=\frac{x^2}{x^2+4}$

F(x) is a function of f(x) and therefore $f(x)=\frac{x}{x+4}$ and F(x) is power 2 of x.

Hence g(x)=x²

In conclusion, $f(x)=\frac{x}{x+4}$ and g(x)=x²

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