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Exercises Functions

Example 6 from Algebra and Trigonometry, 3.4 Composition of Functions

Using a Graph to Evaluate a Composite Function

Using Figure 1, evaluate $f (g (1)) .$

Explanation of the composite function.

Figure 1

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
To evaluate $f (g (1)),$ we start with the inside evaluation. See Figure 2.

Figure 2

We evaluate $g (1)$ using the graph of $g (x),$ finding the input of 1 on the $x -$ axis and finding the output value of the graph at that input. Here, $g (1) = 3.$ We use this value as the input to the function $f .$
$f (g (1)) = f (3)$

We can then evaluate the composite function by looking to the graph of $f (x),$ finding the input of 3 on the $x -$ axis and reading the output value of the graph at this input. Here, $f (3) = 6,$ so $f (g (1)) = 6.$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Using Figure 1, evaluate $g (f (2)) .$

How did it go?

PreviousUsing a Table to Evaluate a Composite Function Next Evaluating a Composition of Functions Expressed as Formulas with a Numerical Input

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 3.4, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.