Name: Block: Date: Pre-Calculus 11 Chapter 5A Functions Lesson #3 Inverse Functions Investigation Consider: () = 1 2 โ4 () = 2 +1 1. In the first column of the table below, enter five ordered pairs of f(x) and g(x). In the second column, interchange the x-coordinates and y-coordinates of the points in the first column. () = 1 2 โ4 () = 2 +1 (x , y) (y , x) 2. Plot the points for the functions f(x) and g(x) for your first column as well as your second column. () = 1 2 โ 4 () = 2 +1 3. What observation can you make about the relationship of the coordinates of your ordered pairs for your first column and second column of f(x) and g(x)? (x , y) (y, x)
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Name: Block: Date: Pre-Calculus 11
Chapter 5A Functions
Lesson #3 Inverse Functions
Investigation
Consider: ๐(๐ฅ) =1
2๐ฅ โ 4
๐(๐ฅ) = ๐ฅ2 + 1
1. In the first column of the table below, enter five ordered pairs of f(x) and g(x). In the second
column, interchange the x-coordinates and y-coordinates of the points in the first column.
๐(๐ฅ) =1
2๐ฅ โ 4 ๐(๐ฅ) = ๐ฅ2 + 1
(x , y) (y , x)
2. Plot the points for the functions f(x) and g(x) for your first column as well as your second
column.
๐(๐ฅ) =1
2๐ฅ โ 4 ๐(๐ฅ) = ๐ฅ2 + 1
3. What observation can you make about the relationship of the coordinates of your ordered
pairs for your first column and second column of f(x) and g(x)?
(x , y) (y, x)
Name: Block: Date: Pre-Calculus 11
Properties of Inverse Functions
Steps of finding the Inverse of a function
Consider: ๐(๐ฅ) =1
2๐ฅ โ 4
๐(๐ฅ) = ๐ฅ2 + 1
Example #1
Consider: ๐(๐ฅ) = 3๐ฅ โ 2
a) Determine ๐โ1(๐ฅ) algebraically
State the domain and range of ๐โ1(๐ฅ).
b) Graph both ๐(๐ฅ) and ๐โ1(๐ฅ) on the same grid
c) Show that (๐(๐โ1(๐ฅ)) = ๐โ1(๐(๐ฅ)) = ๐ฅ
Name: Block: Date: Pre-Calculus 11
Example #2
Consider: ๐(๐ฅ) = ๐ฅ2 โ 4
a) Determine ๐โ1(๐ฅ) algebraically.
State the domain and range of ๐โ1(๐ฅ).
b) Graph both ๐(๐ฅ) and ๐โ1(๐ฅ) on the same grid
c) Show that (๐(๐โ1(๐ฅ)) = ๐โ1(๐(๐ฅ)) = ๐ฅ
d) Is ๐โ1(๐ฅ) a function? If not, describe how the domain of ๐(๐ฅ) could be restricted so that
the inverse of ๐โ1(๐ฅ) becomes a function
Name: Block: Date: Pre-Calculus 11
Example #3
Determine whether the functions in each pair are inverses of each other
a) ๐(๐ฅ) = ๐ฅ โ 4 and ๐(๐ฅ) = ๐ฅ + 4
b) ๐(๐ฅ) = ๐ฅ2 + 1 and ๐(๐ฅ) = โ๐ฅ + 1