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Inverse functions
- Intro Lesson12:05
- Lesson: 111:06
- Lesson: 2a5:00
- Lesson: 2b8:02
- Lesson: 2c15:06
- Lesson: 3a5:12
- Lesson: 3b4:39
- Lesson: 3c4:30
Inverse functions
An inverse function is a function that reverses all the operations of another function. Therefore, an inverse function has all the points of another function, except that the x and y values are reversed.
Related Concepts: Derivative of inverse trigonometric functions, Derivative of logarithmic functions
Lessons
- Introduction
• What is "inverse", and what does "inverse" do to a function?
• Inverse: switch "x" and "y"
• Inverse: reflect the original function in the line "y = x" - 1.Graph an inverse
Given the graph of y=f(x) as shown,
a)Sketch the graph of the inverse y=f−1(x) in 2 ways:
i) by reflecting f(x) in the line y=x
ii) by switching the x and y coordinates for each point on f(x)b)Is f(x) a function?
Is f−1(x) a function? - 2.Inverse of a Quadratic Function
Consider the quadratic function: f(x)=(x+4)2+2a)Graph the function f(x) and state the domain and range.b)Graph the inverse f−1(x) and state the domain and range.c)Is f−1(x) a function?
If not, describe how to restrict the domain of f(x) so that the inverse of f(x) can be a function. - 3.Determine the equation of the inverse.
Algebraically determine the equation of the inverse f−1(x), given:a)f(x)=−5x+4b)f(x)=(7x−8)3−1c)f(x)=2+x3x
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40.
Functions
40.1
Function notation
40.2
Operations with functions
40.3
Adding functions
40.4
Subtracting functions
40.5
Multiplying functions
40.6
Dividing functions
40.7
Composite functions
40.8
Inequalities of combined functions
40.9
Inverse functions
40.10
One to one functions
40.11
Difference quotient: applications of functions