1.
Functions
Imagine functions are like the dye you use
to color eggs. The white egg (x) is put in
the function blue dye B(x) and the result is
a blue egg (y).
2.
The Inverse Function “undoes” what the function
does.
The Inverse Function of the BLUE dye is bleach.
The Bleach will “undye” the blue egg and make it
white.
3.
In the same way, the inverse of a given
function will “undo” what the original
function did.
For example, let’s take a look at the square
function: f(x) = x2
x
33
33
33
f(x)
y
x2
9999
99
99
9
99
999
f--1(x)
33
33
x 33
3
4.
In the same way, the inverse of a given
function will “undo” what the original
function did.
For example, let’s take a look at the square
function: f(x) = x2
x
55
55
55
f(x)
y
x2
25
25 25
25
25
25
25
25
25
255
f--1(x)
55
55
x 55
55
5.
In the same way, the inverse of a given
function will “undo” what the original
function did.
For example, let’s take a look at the square
function: f(x) = x2
x
f(x)
y
121
11
121
121
11
121 121
11
121 121
11
121 121
x2
11
121
121
121
11
121
121
f--1(x)
11
1
111
11
11
x 11
11
11
1
111
6.
Graphically, the x and y values of a
point are switched.
The point (4, 7)
has an inverse
point of (7, 4)
AND
The point (-5, 3)
has an inverse
point of (3, -5)
7.
Graphically, the x and y values of a point are switched.
If the function y = g(x)
contains the points
10
8
6
x
0
1
2
3
4
y
1
2
4
8 16
2
-10
-8
-6
-4
-2
2
-2
4
6
8
10
4
then its inverse, y = g-1(x),
contains the points
-4
x
1
2
4
8 16
-6
y
0
1
2
3
4
-8
-10
Where is there a
line of reflection?
8.
y = f(x)
The graph of a
function and
its inverse are
mirror images
about the line
y=x
y=x
y = f-1(x)
9.
Find the inverse of a function :
Example 1: y = 6x - 12
Step 1: Switch x and y: x = 6y - 12
Step 2: Solve for y:
x = 6y − 12
x + 12 = 6y
x + 12
=y
6
1
x+2= y
6
10.
Example 2:
Given the function : y = 3x2 + 2 find the inverse:
Step 1: Switch x and y: x = 3y2 + 2
Step 2: Solve for y:
x = 3y 2 + 2
2
x − 2 = 3y
x−2
= y2
3
x−2
=y
3
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