Composition of functions ( f * g )( x ) = ? ( g * f)( x ) = ? f( x ) = 1/( x + 3 ) ; g( x ) = x

In order to find the value of the composition of 2 functions, in our case f and g, we have to follow the steps:

Step 1: First, we have to find out the expression of the composition of the 2 functions:

(f*g)(x) = f(g(x))

To find f(g(x)) we have to substitute x by g(x) in the expression of f(x):

f(g(x)) = 1/(g(x) + 3)

Now, we'll substitute g(x) by it's expression:

1/(g(x) + 3) = 1/(x + 3)

f(g(x)) = 1/(x + 3) 

The next step is to calculate (g*f)(x).

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

g(f(x)) = 1/( x + 3 )

Though the composition of 2 functions is not commutative, in this case the results of (f*g)(x) and (g*f)(x) are equal.