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1. WEEK 2 TEACHER
MAE SALVALEON

2. Agenda
today:

5. Perform addition, subtraction,
multiplication, division and composition
of functions

7. Find f(x) = 3x + 4 if x = 2

8. f(x) = 3x + 4 if x = 2
Evaluate:
f(x) = 3x + 4
f(2) = 3(2) + 4
f(2) = 6 + 4
f(2) = 10
Copy the given
Replace x with 2
Perform the operation
answer

9. h(x) = 2x + 1 if x=(3x - 1)
Evaluate:
h(x) = 2x + 1
h(3x - 1) = 2 (3x – 1) + 1
= 6x – 2 + 1
Copy the given
Replace x with (3x-1)
Perform the operation
answer
h(x) = 6x – 1

10. OPERATING
FUNCTIONS
Sum
(f+g)(x) = f(x) + g(x)
Let f and g be any two functions.
Difference
(f-g)(x) = f(x) - g(x)
Product
(fg)(x) = f(x) ∙ g(x)
Quotient
{f/g}(𝑥) = f(x)/g(x)
where g(𝑥) ≠0

11. Let’s Solve
Operating Functions
Let f and g be any functions.
1. Sum:
(f+g)(x) = f(x) + g(x)
Solution:
= (4x+3) + (3x-2)
= 4x+3+3x-2
= 7x+1
f(x) = (4x+3) and g(x) = (3x-2).

12. Let’s Solve
Operating Functions
Let f and g be any functions. f(x) = (4x+3) and g(x) = (3x-2).
2. Difference:
(f-g)(x) = f(x) - g(x)
Solution:
= (4x+3) - (3x-2)
= 4x+3-3x+2
= x+5

13. Let’s Solve
Operating Functions
Let f and g be any functions. f(x) = (4x+3) and g(x) = (3x-2).
3. Product:
(fg)(x) = f(x) ∙ g(x)
Solution:
= (4x+3) ∙ (3x-2)
= 12x2+x-6
= 12x2 - 8x + 9x - 6

14. Let’s Solve
Operating Functions
Let f and g be any functions. f(x) = (4x+3) and g(x) = (3x-2).
4. Quotient:
f
g
𝑥 =
f x
g x
, where g 𝑥 ≠ 0
Solution:
=
(4𝑥+3)
(3𝑥−2)
(since the expression isn’t factorable, so that will be the final answer)

15. Let’s Learn
Composition of
Functions
The composition of function is denoted by;
𝑓 °𝑔 and is defined by the equation
(𝑓 °𝑔) (𝑥) = 𝑓 (𝑔(𝑥))
𝑔 ° 𝑓 and is defined by the equation
(𝒈 ° 𝒇) (𝒙) = 𝒈 (𝒇(𝒙))

16. Let’s Solve
Composition of
Functions
Let f and g be any functions.
5. 𝑓 circle 𝑔
(𝑓 °𝑔) (𝑥) = 𝑓 (𝑔(𝑥))
Solution:
= (4(3x-2)+3)
= 12x - 5
f(x) = (4x+3) and g(x) = (3x-2).
= 12x - 8 + 3

17. Let’s Solve
Composition of
Functions
Let f and g be any functions.
6. 𝑔 circle 𝑓
(𝑔 ° 𝑓) (𝑥) = 𝑔 (𝑓(𝑥))
Solution:
= (3(4x+3)-2)
= 12x + 7
f(x) = (4x+3) and g(x) = (3x-2).
= 12x + 9 - 2

18. What’s more
Composition of
Functions
Let h and g be any function, h(x) = (x+4)2 and g(x) = √𝒙.
7. (h ° g) (𝑥) = h (g(𝑥)) 8. (𝑔 ° h) (𝑥) = 𝑔 (h(𝑥))

19. Try This 9. If f(x) = 5x + 3 and g(x) = 3x2, solve for f(g(4)).
Solution;
Solveforg(4),wherethevalueofourx=4.
g(x)=3x2
g(4)=3(4)2
g(4)=3(16)
g(4)=48
Now,f(g(4))=f(48),wherethevalueofourx=48.
f(x)=5x+3
f(48)=5(48)+3
f(48)=240+3
f(48)=243 ; hence,f(g(4))=243

21. May we have fun and productive
learning sessions ahead.
Welcome to General Mathematics!