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- CLEP College Algebra
- Composite Functions and Inverses
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