This is a simple process to combine more than two Functions with the help of addition, subtraction, multiplication and division. There is another way also to combine two Functions that is the composite functions.
Composite function is the result of one function in the form of other function. This is expressed by the small Circle. Suppose that there are two functions ‘f’ and ‘g’, Then the composite function ‘f’ to ‘g’ is denoted as (g o f) (x) or sometimes as g (f (x). This can not be denoted by a simple dot other wise the meaning would be the produce in spite of composition.
If g (x) is given in the problem then Composite Functions is denoted as f (g(x)) = f o g (x). Here it should be noticed that f (g(x)) is not equal to the g (f (x)).
A function can be composite with the self and is written as (f o f) (x) that is f (f (x)). Any function works only under its Domain. A domain is the Set of all the values that are covered by the function.
To find the domain of the composite function one needs to remind some Point. Suppose that there is a composite function g (f (x)) the:
First make sure that the domain of the function f (x) should be obtained first.
Then the domain of the other function ‘g’ is defined according to the first function f (x).
While the evaluation of a function if a function f (x) is given to us and asked to find the value of the function f(2), we replace ‘x’ with 2 in the function. Similarly if our notation for the composite functions is f (g(x)) and we have to calculate the ‘f’ function then we will replace the ‘x’ with g (x) everywhere. This is not so different from the evaluation process.