Math Lesson 16.4.3 - Evaluating Composite Functions

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Welcome to our Math lesson on Evaluating Composite Functions, this is the third lesson of our suite of math lessons covering the topic of Composite Functions, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.

Evaluating Composite Functions

Evaluating a composite function means finding the value of that composite function for a given input x. For example, g ◦ f (3) means calculating the value of g[f(x)] for x = 3. Let's consider an example to clarify this point.

Example 2

For the functions

and

calculate

1. f ◦ g (3)
2. g ◦ f (4)

Solution 2

1. First, we have to find the general form of the given composite function, i.e. f ◦ g(x). Thus,
   f ∘ g(x) = f[g(x)]
   = √x² - 3x
   Therefore, for x = 3 we have
   f ∘ g(3) = f[g(3)]
   = √3² - 3 ⋅ 3
   = √9 - 9
   = 0
2. First, we have to find the general form of the given composite function, i.e. g ◦ f(x). Thus,
   g ∘ f(x) = g[f(x)]
   = (√x)² - 3√x
   = x - 3√x
   Therefore, for x = 4 we have
   g ∘ f(4) = g[f(4)]
   = 4 - 3√4
   = 4 - 3 ⋅ 2
   = 4 - 6
   = -2

You have reached the end of Math lesson 16.4.3 Evaluating Composite Functions. There are 9 lessons in this physics tutorial covering Composite Functions, you can access all the lessons from this tutorial below.

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6. Continuing learning functions - read our next math tutorial: Piecewise Functions

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