If f(x) = x^2+3 g(x) =sqrt(x) determine (fog)(x) and (gof)(x).

We compose the 2 given functions in this
way:

(fog)(x) = f(g(x))

We
notice that the variable x was replaced by the function g(x). According to this, we'll
write the function f(g(x)) by substituting x by g(x) in the  original expression of
f(x):

f(g(x)) = [g(x)]^2 +
3

f(g(x)) = (sqrt x)^2 +
3

(fog)(x) = f(g(x)) = x +
3

Now, we'll compose gof and we'll
get:

(gof)(x) = g(f(x))

We
notice that the variable x was replaced by the function f(x). According to this, we'll
write the function g(f(x)) by substituting x by f(x) in the  original expression of
g(x):

g(f(x)) = sqrt
f(x)

(gof)(x) = g(f(x)) = sqrt
(x^2+3)

As we can remark, the result of the
2 compositions is not the same!