Richland Community College Finding the Inverse of Each Function Questions

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Name
Class
Date
6-1 CLASSWORK
Inverse Relations and Functions
Inverse operations “undo” each other. Addition and subtraction are inverse
operations. So are multiplication and division. The inverse of cubing a
number is taking its cube root.
• If two functions are inverses, they consist of inverse operations performed in the
opposite order
Problem
What is the inverse of the relation described by f(x)=x+1?
f(x)=x+1
y=x+1
Rewrite the equation using y, if necessary.
x= y + 1
Interchange x and y.
x-1= y
Solve for y.
y = x-1
The resulting function is the inverse of the original function.
So, f'(x) = x-1.
Find the inverse of each function.
1. y= 4x – 5
2.
y = 3r? +
2
3. f(x) = 2(x – 5)2
4.
y = √x+4
6-1 CLASSWORK (continued)
Inverse Relations and Functions
F1
Examine the graphs of S(x) – VX-2 and its inverse, f ‘(x) = x2 + 2, at the
right.
Notice that the range of f and the domain off lare the set of all real
numbers x 20.
Similarly, the domain off and the range off the same: the set of all real
numbers x>2.
This inverse relationship is true for all relations whenever both fand flare
defined.
0 123
Problem
What are the domain and range of the inverse of the function /(x) = 13 – x?
fis defined for 3-x>0 orx 0. So, the domain off’ is the set of all x 20.
Y
6
3-2-1012
Name the domain and range of the inverse of the function.
5. y=2x-1
y = x +5
6.
y = v=x+8
8. y=(x-6)
7.