Evaluating Functions

1. Question of the Day
Given ℎ(𝑥)= 𝑥2 − 7𝑥 and 𝑟(𝑥)= 𝑥2 + 𝑥 − 1,
find (ℎ + 𝑟)(𝑥).
a. 2𝑥2 – 1
b.2𝑥2 - 6𝑥 – 1
c. 2𝑥4 + 6𝑥2 – 1
d.2𝑥2 + 6𝑥 – 1

2. General Mathematics
LESSON 3
Operations on Function

3. Lesson Objectives
After studying this lesson, you should be able to:
a. define operations on functions;
b. identify the different operations on functions; and
c. perform addition, subtraction, multiplication,
division, and composition of functions.

4. Review

5. Tell whether each statement is True or
False.
1. The function notation 𝑦 = 𝑓(𝑥) tells you
that y is a function of x.
2. The notation 𝑓(𝑥) means “f times x”.
3. To evaluate a function, simply replace
the value of x with the given number.
4. If 𝑓(𝑥) = 𝑥 + 8, then 𝑓(−2) is 6.
5. If 𝑓(𝑥) = −3𝑥 + 4, then 𝑓(5) is -19

7. Operations
on Functions

8. Definition. Let f and g be functions.
1. Their sum, denoted by 𝑓+𝑔, is the function
denoted by
(𝑓+𝑔)(𝑥) =𝑓(𝑥)+𝑔(𝑥).
2. Their difference, denoted by 𝑓−𝑔, is the
function denoted by
(𝑓−𝑔)(𝑥)=𝑓(𝑥)−𝑔(𝑥).

9. Given the functions:
𝑓(𝑥)=𝑥+5 𝑔(𝑥)=2𝑥−1
Determine the following
functions:
a. (𝑓+𝑔)(𝑥)
b. (𝑓−𝑔)(𝑥)

10. Let 𝑓(𝑥) = 2𝑥 − 3 and 𝑔(𝑥) = 𝑥2 − 5,
find;
a. (𝑓+𝑔)(𝑥)
b. (𝑓−𝑔)(𝑥)

11. 3. Their product, denoted by 𝑓•𝑔, is the
function denoted by
(𝑓•𝑔)(𝑥)=𝑓(𝑥)•𝑔(𝑥).
4. Their quotient, denoted by 𝑓/𝑔, is the
function denoted by
(𝑓/𝑔)(𝑥)=𝑓(𝑥)/𝑔(𝑥), excluding the values of x
where 𝑔(𝑥)=0.

12. Given the functions:
𝑓(𝑥)=𝑥+5 𝑔(𝑥)=2𝑥−1 and
ℎ(𝑥)=2𝑥2+9𝑥−5
Determine the following
functions:
a. (𝑓∙𝑔)(𝑥)
b. (h/𝑔)(𝑥)

13. If 𝑓(𝑥) = 3𝑥 + 2 and
𝑔(𝑥) = 𝑥2 + 3𝑥 − 4, find;
Determine the following
functions:
a. (𝑓∙𝑔)(𝑥)
b. (f/g)(𝑥)

14. 5. The composite function denoted by (𝑓
∘ 𝑔)(𝑥)=𝑓(𝑔(𝑥)). The process of obtaining a
composite function is called function
composition.

15. Given the functions:
𝑓(𝑥)=𝑥+5 𝑔(𝑥)=2𝑥−1
Find:
a. (𝑓 ∘ 𝑔)(𝑥)
b. (g ∘ 𝑓)(x)

16. Let 𝑓(𝑥) = 2𝑥 − 3 and 𝑔(𝑥) = 𝑥2 − 5,
find;
a. (𝑓 ∘ 𝑔)(𝑥)
b. (g ∘ 𝑓)(x)

17. Quiz

19. Question of the Day
Given ℎ(𝑥)= 2𝑥2 − 7𝑥 and 𝑟(𝑥)= 𝑥2 + 𝑥 − 1,
find (ℎ + 𝑟)(𝑥).
a. 2𝑥2 – 1
b.3𝑥2 + 6𝑥 – 1
c. 3𝑥4 − 6𝑥2 – 1
d.3𝑥2 −6𝑥 – 1

20. Answer:
D. 3𝑥2 −6𝑥 – 1