Module#8 notes

1. MATHEMATICAL KEY POINTS…
 Definition of One-to-One Function
The function is one-to-one if for any in the domain of , then ( ) ( ). That is, the
same value y-value is never paired with two different x-values.
EXAMPLES:
1)
2) ( ) *( ) ( ) ( ) ( ) ( )+
3) The relation pairing of an SSS member to his/her SSS number
4)
x 1 2 4 8 9
y 3 0 1 6 2
 Definition of an Inverse Function
Let be a one-to-one function with domain A and range B. Then the inverse of , denoted by , is a
function with domain B and range A. It is defined by ( ) if and only if ( ) for any in B.
EXAMPLES:
RELATION INVERSE
A
( ) *( ) ( ) ( ) ( ) ( )+ ( ) *( ) ( ) ( ) ( ) ( )+
x 1 2 4 8 9
y 3 0 1 6 2
3 0 1 6 2
1 2 4 8 9
4
2
3
16
4
3

2.  Determining the Inverse of a Function from its Equation
o Write the function in the form ( )
o Interchange the and variables
o Solve for in terms of
EXAMPLE: Solve for the inverse of the following functions below.
1) ( )
Solution:
( ) *Given
* Write the function in the form ( )
* Interchange the and variables
* Solve for in terms of
( )
*the inverse function of ( )