# 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*?

Solution:

*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)?*

Solution:

*f◦g(x) = f(g(x))*

$latex* *f(x) = 1-x$

Worked Problem 3: MMC Elimination 2013

If , find *f(x)*

Solution:

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.

Let y=g(x)

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,

Now, let

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.

### Dan

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