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

### 1 Answer | Add Yours

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!

### Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes