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Dividing functions
- Lesson: 1a4:19
- Lesson: 1b4:09
- Lesson: 1c5:02
- Lesson: 1d3:29
- Lesson: 2a3:27
- Lesson: 2b23:37
- Lesson: 2c3:52
- Lesson: 3a5:14
- Lesson: 3b12:29
Dividing functions
Basic Concepts: Dividing rational expressions, Function notation (Advanced), Operations with functions
Related Concepts: Quotient rule
Lessons
Dividing functions: (gf)(x)=g(x)f(x)
- 1.Determine the Quotient of Two Functions and State Its Domain
Write an expression in the simplest form for (gf)(x)
State the domain restrictionsa)f(x)=3x−8g(x)=x+2b)f(x)=4x3+5x2g(x)=xc)f(x)=2x2+4x−30g(x)=2x−6d)f(x)=x−3g(x)=x2+2x−15 - 2.Operations of Functions – In a Nutshell
Consider the functions f(x)=x+5xand g(x)=x−23xa)state the domain of f(x)and g(x)b)write an expression in the simplest form for each
of the following and state the domains
i) (f+g)(x)
ii) (f−g)(x)
iii) (fg)(x)
iv) (gf)(x)c)evaluate (gf)(4)in 2 different ways - 3.Sketch the Quotient of Two Functions
Consider the functions f(x)=2x2+4x−30
g(x)=20x−60a)Determine the equation of the function
h(x)=(fg)(x) and state the domain restrictionsb)Sketch the graph ofh(x)=(fg)(x)
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2.
Functions
2.1
Function notation
2.2
Operations with functions
2.3
Adding functions
2.4
Subtracting functions
2.5
Multiplying functions
2.6
Dividing functions
2.7
Composite functions
2.8
Inequalities of combined functions
2.9
Inverse functions
2.10
One to one functions
2.11
Difference quotient: applications of functions