The document discusses operations that can be performed on functions, including addition, subtraction, multiplication, division, and composition. It defines each operation and provides examples of how to find the sum, difference, product, quotient, and composite of functions. The domain of operations on functions is also discussed.

1. OPERATIONS ON
FUNCTION

2. LESSON OBJECTIVES
At the end of the lesson, the students must be able to:
• find the sum of functions;
• determine the difference between functions;
• identify the product of functions;
• find the quotient between functions; and
• determine the composite of a function.

3. OPERATIONS ON FUNCTIONS
In this definition, new functions are
formed from the given functions by adding,
subtracting, multiplying and dividing
function values. These new functions are
called sum, difference, product and quotient
of the original functions.

4. 4
Operations on Functions
LET F(X)AND G(X) BE ANY
FUNCTIONS.
1. Addition:
2. Subtraction:
3. Multiplication:
4. Division:
5. Composition of Functions:
( )( ) ( ) g(x)
f g x f x
  
( )( ) ( ) g(x)
f g x f x
  
( )( ) ( )g(x)
fg x f x

( )
( ) , ( ) 0
( )
f f x
x g x
g g x
 
 
 
 
wherein the function f(x) replaces all input variables in g(x).
( ) or (
] [
[ ]
)
g g f
x x
f

5. J.T.HORTELANO,MAT-Math General Mathematics 5
DOMAIN OF OPERATIONS ON
FUNCTIONS
f g
f g
f
f
g
g
D
D
D
D


}
Intersection of the
domains of f and g,
with the added
restriction on the
quotient function
where f/g is
undefined.
g
f
D D
f g
D
Consists of the set of values of x for which g(x) is
contained in the domain of f.

6. Illustrative Examples:
1. Given f(x) = x + 1 and g(x) = x2 – x – 2, find the
following:
a. (f+g)(x)
b. (f – g)(x)
c. (f*g)(x)
d. (f/g)(x)
e. (f∘g)(x)

7. 7
LET’S TRY
THIS!
Let
Define the following functions and determine the domain of each.
1. f+g
2. f/h
3. g-f
4. g(f(-2))
5. h(f(5))
𝑓(x) = 𝑥 − 1, 𝑔(𝑥) = 3𝑥2−2, and ℎ(𝑥) = 𝑥.

8. SEATWORK:
Given the following functions, perform the indicated operations.
f(x) = x2 – 14x + 49 g(x)= x - 7
h(x)= x -1 k(x) = x + 5
1. (f + g)(x)
2. (f * k)(x)
3. (f/g)(x)
4. (k- h)(x)
5. (f ∘ h)(x)