If f(x) = x^2 + 5 and g(x) = sqrt(2x) then find (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 +
5

f(g(x)) = (sqrt 2x)^2 +
5

(fog)(x) = f(g(x)) = 2x +
5

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
2f(x)

(gof)(x) = g(f(x)) = sqrt
2(x^2+5)

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