Function composition: The next topic that we have to discuss here is that of function composition. The composition of f(x) & g(x) is
( f o g ) ( x ) = f ( g ( x ))
In other terms, compositions are evaluated by plugging the second function listed in the first function listed. Note that order is significant here. Usually interchanging the order will result in a different answer.
Example Given f ( x ) = 3x^{2 }- x = 10 and g ( x ) = 1 - 20 x determine each of the following.
(a) (f o g ) (5)
(b) ( f o g ) ( x )
Solution
(a) (f o g) (5)
In this case we've got a number rather than an x but it works in precisely the same way.
( f o g ) (5) = f (g (5))
= f ( -99) = 29512
= f (1 - 20x )
= 3(1 - 20x )^{2} - (1 - 20 x ) + 10
= 3(1 - 40x + 400 x^{2} ) -1 + 20 x + 10
= 1200 x^{2} -100 x + 12
Compare this answer to the next part & notice that answers are NOT the similar. The order wherein the functions are listed is important!