Tuesday, May 29, 2012

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.

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