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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
Do better in math today
7.
Functions
7.1
Function notation
7.2
Operations with functions
7.3
Adding functions
7.4
Subtracting functions
7.5
Multiplying functions
7.6
Dividing functions
7.7
Composite functions
7.8
Inequalities of combined functions
7.9
Inverse functions
7.10
One to one functions
7.11
Difference quotient: applications of functions