1.05 - Operations on Functions

University:
High School
Course:
High School Physics
Academic year:

2024
Views:

157

Pages:

11
Author:

1 1

1.05 Operations on Functions •Use Brackets •Order Matters •Follow BEDMAS •Simplify wherever possible The ‘Rules’ 𝑓+𝑔 𝑓+𝑔 𝑥 𝑓 𝑥 + 𝑔(𝑥) • Example: • 𝑓 𝑥 = 2𝑥 − 3 • 𝑔 𝑥 = 𝑥 2 − 8𝑥 + 7 𝑓+𝑔 = 2𝑥 − 3 + 𝑥 2 − 8𝑥 + 7 = 𝑥 2 − 6𝑥 + 4 Addition 𝑓+𝑔 • Example: • 𝑓 𝑥 =8 𝑥−3 −3 • 𝑔 𝑥 =3 𝑥+2 2−5 𝑓+𝑔 𝑥 𝑓+𝑔 3 = 𝑓 3 + 𝑔(3) 𝑓 𝑥 + 𝑔(𝑥) 𝑓 3 =8 3−3 −3 = −3 𝑔 3 =3 3+2 2−5 = 70 Addition 𝑓 3 + 𝑔(3) = −3 + 70 = 67 𝑓−𝑔 𝑓−𝑔 𝑥 𝑓 𝑥 − 𝑔(𝑥) Subtraction • Example: • 𝑓 𝑥 = 2𝑥 − 3 • 𝑔 𝑥 = 𝑥 2 − 8𝑥 + 7 𝑓−𝑔 = 2𝑥 − 3 − 𝑥 2 − 8𝑥 + 7 = 2𝑥 − 3 − 𝑥 2 + 8𝑥 − 7 = −𝑥 2 + 10𝑥 − 10 • Example: 𝑓−𝑔 𝑓−𝑔 𝑥 𝑓 𝑥 − 𝑔(𝑥) Subtraction • 𝑓 𝑥 = 1 2 − 𝑥−2 • 𝑔 𝑥 = 𝑥 2 + 3𝑥 (𝑓 − 𝑔)(𝑥) 1 = − 𝑥 − 2 − 𝑥 2 + 3𝑥 2 1 = − 𝑥 − 2 − 𝑥 2 − 3𝑥 2 1 2 = −𝑥 − 3𝑥 + − 𝑥−2 2 𝑓⋅𝑔 𝑓⋅𝑔 𝑥 𝑓 𝑥 ⋅ 𝑔(𝑥) • Example: • 𝑓 𝑥 = 2𝑥 − 3 • 𝑔 𝑥 = 𝑥−1 𝑓⋅𝑔 = 2𝑥 − 3 𝑥−1 = 2𝑥 𝑥 − 1 − 3 𝑥 − 1 Multiplication 𝑓⋅𝑔 • Example: • 𝑓 𝑥 = 2𝑥 − 3 • 𝑔 𝑥 = 𝑥−1 𝑓⋅𝑔 𝑥 𝑓(3) ⋅ 𝑔(3) = 2(3) − 3 = 3 𝑓 𝑥 ⋅ 𝑔(𝑥) (3) − 1 2 = 2𝑥 𝑥 − 1 − 3 𝑥 − 1 = 2(3) (3) − 1 − 3 (3) − 1 =6 2−3 2 =3 2 Multiplication 𝑓 ÷ 𝑔 or 𝑓 𝑔 𝑓÷𝑔 𝑥 𝑓 𝑥 𝑔 𝑥 Division • Example: • 𝑓 𝑥 = 3 𝑥−2 • 𝑔 𝑥 =− 𝑥−5 −2 𝑔 (𝑥) 𝑓 − 𝑥−5 −2 = 3 𝑥−2 𝑥−2 = − 𝑥−5 −2 3 −𝑥 𝑥 − 5 + 2 𝑥 − 5 − 2𝑥 + 4 = 3 3 𝑓 10 = 8 𝑔 10 = −7 • Example: • 𝑓 𝑥 = 𝑓 ÷ 𝑔 or 𝑓 𝑔 𝑓÷𝑔 𝑥 𝑓 𝑥 𝑔 𝑥 Division 3 𝑥−2 • 𝑔 𝑥 =− 𝑥−5 −2 𝑔 (𝑥) 𝑓 −𝑥 𝑥 − 5 + 2 𝑥 − 5 − 2𝑥 + 4 = 3 𝑔 (10) 𝑓 −10 10 − 5 + 2 10 − 5 − 2(10) + 4 = 3 −50 + 10 − 20 + 4 = 3 −56 = 3 •Visions 1 •P26: 4ace, 6 •P56: 15a •P68: 7ac Homework