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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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24.
Functions
24.1
Function notation
24.2
Operations with functions
24.3
Adding functions
24.4
Subtracting functions
24.5
Multiplying functions
24.6
Dividing functions
24.7
Composite functions
24.8
Inequalities of combined functions
24.9
Inverse functions
24.10
One to one functions
24.11
Difference quotient: applications of functions