Inverse Functions.notebook
April 28, 2021
Quiz Outline:
• Thursday, April 29 at 12:20pm
• 1 hour
• 11 questions, 5 multiple choice, 6 written response
Lesson: Inverse Functions
Topics:
• Key features of Functions and Representations of Functions
• Identify if it is a Function, Domain and Range­ equation, graph, set of ordered pairs,
mapping diagram
• Evaluate using function notation (i.e. f(x) = 5x + 9, evaluate f(4))
• Different types of functions ­ linear, quadratic, rational, radical and absolute
Nov 21­8:16 AM
Apr 28­12:30 PM
Characteristics of an Inverse Function
Inverse Function: the reverse of the original function
• To determine the inverse of a function, switch the variables
and solve for y.
• f­1 is the notation used for the inverse function of f
Example 1: Determine the inverse of the following functions.
Investigate: Complete the following table of values.
y = 2x ­ 1
x
a. f(x) = 3x + 1
x = 2y ­ 1
x
y
b. f(x) = ¾x ­ 6
Let f(x) = y
Let f(x) = y
y
­2
­2
­1
­1
0
0
1
1
2
2
Switch the x and y variables
Isolate for y.
Nov 21­8:19 AM
Characteristics of an Inverse Function
Nov 21­8:23 AM
Characteristics of an Inverse Function
• The inverse function is not necessarily a function
• The domain of a function f is equal to the range of f­1
• The range of a function f is equal to the domain of f­1
Example 2: Determine the inverse of the following function.
Example 3a: State the domain and range of the function and its
inverse.
a. f(x) = x2 ­ 1
Let f(x) = y.
b. f(x) = (x ­ 5)2 ­ 3
f(x) = x2 ­ 1
Let f(x) = y.
Source: https://www.desmos.com/calculator
Source: https://www.desmos.com/calculator
The inverse is not a function because
it does not pass the vertical line test
(refer to graphs on next slide)
Nov 21­8:23 AM
Nov 21­8:23 AM
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Inverse Functions.notebook
April 28, 2021
Characteristics of an Inverse Function
Characteristics of an Inverse Function
• The graph of an inverse function f­1 is a reflection of the
function f along the line y = x.
• The domain of a function f is equal to the range of f­1
• The range of a function f is equal to the domain of f­1
Example 4:
a. Graph the line y = x.
Example 3b: State the domain and range of the function h(x) and its
inverse given the following:
b. Graph the following function and its inverse.
Let d(x) = y
h(x)
d(x) = x ­ 3
4
h­1(x)
Domain
Range
Nov 21­8:23 AM
Nov 21­8:23 AM
Characteristics of an Inverse Function
• The graph of an inverse function f­1 is a reflection of the
function f along the line y = x.
Example 5: Given the value of f(x) = k(2 + x), find the value of k
if f­1(­2) = ­3.
Example 4:
a. Graph the line y = x.
b. Graph the following function and its inverse.
A coordinate on the inverse function (f­1) is (­2, ­3)
Therefore, a coordinate on the function f(x) is the opposite (­3, ­2)
Source: Functions 11, Nelson. Nelson Education, Inc., 2008.
Source: https://www.desmos.com/calculator
Nov 21­8:23 AM
Nov 21­8:42 AM
Student Demos Activity: Card Sort: Inverse Functions
Nov 21­9:11 AM
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