Operating Composite Functions
In the previous posts I gave overviews about domain and range as well as how to determine whether an equation is a function or not. This time let’s talk about operating composite functions. Composite functions are combination of two or more functions.
Worked Example 1:
Given , What is h◦g?
h◦g means h that is compose of g(x)
h◦g = h(g(x))
Worked Problem 2: (Metrobank -MTAP Dep-Ed Math Challenge Elimination)
If and , what is f◦g(2)?
f◦g(x) = f(g(x))
$latex f(x) = 1-x$
Worked Problem 3: MMC Elimination 2013
If , find f(x)
Let . This will reduce the relation to
Let’s start with , We need to find the value of x here to make it only x. Meaning, we will look for a specific expression in x to substitute. We do trial and error. Let x=x+1,etc. But of course that is so impractical. Try this out.
We solve for x in terms of y. Why? Because that is the value of x that will make the expression become x.
But that is not the answer yet,
Since we are just working with x’s we need to drop all y’s and put x instead.
Going back to the original problem,
Manipulating this we get
This is the required answer. But if the problem ask for etc. From f(x) you can let x=x+1 and so on.