Given two functions, $f(x)$ and $g(x)$, both functions can create composite functions $fg$ and $gf$.

Composite function $fg$

Composite function of $fg$ can be formed by substituting the function of g into the function of f.

One condition must be satisfied, range of g is within the domain of f ($R_g\subseteq D_f$)

Composite function $gf$

Composite function of $gf$ can be formed by substituting the function of f into the function of g.

One condition must be satisfied, range f is within the domain of g ($R_f\subseteq D_g$)