Composite Functions (3.18.2)

Question 1

• A composite function is made up of multiple functions acting on each other in a specified order.

Answer 1

• A composite function is made up of multiple functions acting on each other in a specified order.

Question 2

• The benefit of composing functions with each other is that you can follow one input through several processes to reach a final output.

Answer 2

• The benefit of composing functions with each other is that you can follow one input through several processes to reach a final output.

Question 3

• Composition notation: indicates that f (x) will be evaluated with the output from g (x).

Answer 3

• Composition notation: indicates that f (x) will be evaluated with the output from g (x).

Question 4

• Note carefully which function is going to be used first. Make sure that the first function’s output is used in the second function.

Answer 4

• Note carefully which function is going to be used first. Make sure that the first function’s output is used in the second function.

Question 5

The composition, g of f, is being evaluated here at
x = 3.
First f (x) is evaluated for x = 3. The answer is 8. Next, g(x)
is evaluated for x = 8. The answer is 137.

So, g*f(3) = 137.

In this example, the composition is f of g.
So, first evaluate g (x) for x = 3. The answer is 22. Next
evaluate f (x) for x = 22. The answer is 65.
Therefore, f*g(3) = 65.

Answer 5

The composition, g of f, is being evaluated here at
x = 3.
First f (x) is evaluated for x = 3. The answer is 8. Next, g(x)
is evaluated for x = 8. The answer is 137.

So, g*f(3) = 137.

In this example, the composition is f of g.
So, first evaluate g (x) for x = 3. The answer is 22. Next
evaluate f (x) for x = 22. The answer is 65.
Therefore, f*g(3) = 65.