ABSTRACT
EXAMPLE 15.1: Consider the functions f and g given by the rules f (x) = cos x and g(x) = ex then (g o f)(x) = g (f (x)) = g(cos x) = erns x while (f g)(x) = f (g(x)) = cos(g(x)) = cos(ex). Clearly, gof and fog are not equal functions since (g o f) (x) > 0 for all x E El . On the other hand, f (g(x)) = cos(ex) is negative for some x, in particular for x = 1. So composition of functions is not commutative.
