This document discusses functions and operations that can be performed on functions. It defines a function as a relation that assigns each input exactly one output. The four basic operations that can be performed on functions are addition, subtraction, multiplication, and division. Examples are provided to demonstrate how to apply these operations by combining two functions using the notation for each operation. The key is to apply the operation to the outputs of each function using the same input. Several practice problems are then given for the student to work through.

1. GENERAL MATHEMATICS
Prepared By:
Sir Jet

2. A function is a relation that assigns to each input value
exactly one output value. Like numbers and polynomials
we can add, subtract, multiply and divide functions which
results into a new function. Several functions can work
together in one larger function. There are 5 common
operations that can be performed on functions. The four
basic operations on functions are adding, subtracting,
multiplying, and dividing. The notation for these
functions is as follows:
 Addition (f + g)(x) = f(x)+ g(x)
 Subtraction (f − g)(x)= f(x) − g(x)
 Multiplication (f · g)(x)= f(x) ∙ g(x)
 Division
𝒇
𝒈
(x) =
𝒇(𝒙)
𝒈(𝒙)

3. Example: Given P(x) = 4 -2x and Q(x) = 9 –x2,
find (a) P(x) + Q(x)
(b) P(x) - Q(x)
(c) P(x)Q(x)
(d)
𝑷(𝒙)
𝑸(𝒙)
(a) P(x) + Q(x) = (4-2x) + (9 –x2) = 13 – 2x –x2
(b) P(x) - Q(x) = (4-2x) - (9 –x2) = x2 -2x - 5
(c) P(x)Q(x) = (4-2x) (9 –x2) = 2x3 – 4x2 – 18x +36
(d)
𝑷(𝒙)
𝑸(𝒙)
=
(4−2x)
(9 –x2)

4. Your turn!
Let f(x) = x + 1 and g(x) = 2x + 1,
find (a) f(x) + g(x)
(b) f(x) - g(x)
(c) f(x)g(x)
(d)
𝒇(𝒙)
𝒈(𝒙)

5. Example 1. f(x) = x 2 − x − 2 and g(x)= x +1 ,
find (f + g)( − 3)

6. Your turn!
f(x) = 2x2 + 3x – 4 and g(x) = 2x + 3,
find (f + g) (2)

7. Example 2. f(x)= 2x − 4 and g(x)= x2 − x + 5,
find (f – g)(4)

8. Your turn!
f(x) = 2x2 + 3x – 4 and g(x) = 2x + 3,
find (f – g) (3)

9. Example 2. h(x) =2x − 4 and k(x) = − 3x + 1
Find (h · k)(5)

10. Your turn!
g(x) = 3x + 1 and f(x) = x3 + 3x2
Find g(2)· f(2)

11. Example 2. h(n) = 2n − 1 and g(n) = 3n − 5
Find
h(n)
g(n)
(0)

12. Your turn!
f(a) = − 2a − 4 and g(a) = a2 + 3
Find (
𝒇
𝒈
)(7)

13. Seatwork: by pair
1) g(a) = a3 + 5a2 and f(a) = 2a + 4. Find g(3)+ f(3)
2) d(x) = 4x + 3 and s(x) = x3 − 2x2 . Find (d−s)( − 1)
3) t(x) = 5x + 1 and r(x) = x + 3x2 . Find t(2)· r(2)
4) g(n) = n2 + 5 and f (n) = 3n + 5. Find
𝒈(𝒏)
𝒇(𝒏)

14. For numbers 5-8
Let f(x) = x + 2and g(x) = x2 + 1,
find (a) f(x) + g(x)
(b) f(x) - g(x)
(c) f(x)g(x)
(d)
𝒇(𝒙)
𝒈(𝒙)

15. Assignment: 1 whole