Express the following function, F(x) as a composition of two functions and f and g.
f(x)= x^2/(x^2+4)
how about we let
f(x) = x^2
g(x) = x/(x+4)
then g(f(x))
g(x^2)
= x^2/(x^2 + 4)
To express the function F(x) as a composition of two functions, let's first define another function g(x).
Let g(x) = 1/x.
Now, we can express F(x) as a composition of f and g.
F(x) = f(g(x))
Substituting the definition of f(x) and g(x) into the expression for F(x), we have:
F(x) = f(g(x)) = f(1/x) = (1/x)^2/((1/x)^2 + 4)
Simplifying, we get:
F(x) = (1/x^2)/(1/x^2 + 4)
Therefore, the function F(x) can be expressed as a composition of f and g as F(x) = (1/x^2)/(1/x^2 + 4).