# Question #715a8

##### 1 Answer

#### Explanation:

This is a composition of functions. It is essentially a function within a function. The notation states that you are evaluating the inner function, g(x), and then inserting the result into f(x) and re-evaluating.

Read it as "f of g". I prefer the second notation as you can see which one is inside the other.

To evaluate, you replace all the

As an example, let's evaluate

i) Evaluate the inner function

ii) Insert this into the outer function and evaluate

But now that we have the composition function, we can insert

*As extra but vital information, an important rule for the composition to be defined is this:

I.e.

This says that the range of

In this case,

The below statement is true, so the composition is defined.