INVERSE OF ONE-TO-ONE FUNCTIONS (that will help you)

inverse of one-to-one function

2. REVIEW
Write ONE-TO-ONE on the blank if the relation shows
one-to-one function and NOT if it is not a one-to-one
function.
_______1. True or False Questions to answers.
_______2. Teacher to his students.
_______3. LRN (Learners Reference Number) to
students. _______4. Sim Card to its mobile number.
_______5. The relation pairing a country to its capital.

3. INVERSE OF
ONE-TO-ONE
FUNCTION

4. OBJECTIVE:
At the end of the lesson you
must be able to:
a.) define inverse function;
b.) determines the inverse of
a one-to-one function.
(M11GM-Id-2)

5. Note: A function has an inverse if and only
if it is one-to-one function.

8. To find the inverse of a one-to-one
function, consider the following:
a. Express the function in the form
�= ??????(�);
b. Interchange the x and y variables in the
equation;
c. Solve for y in terms of x.
d. Replace the new y with ??????
−1
(�)

9. EXAMPLE
Find the inverse of ??????(�)=2�+3.
Solution.
(1) Express the function in the form �=??????(�):
�=2�+3
(2) Interchange the x and y variables:
�=2�+3

10. (3) Solve for y in terms of x:
�=2�+3
−1(−2�=−�+3)
2�
2
=
�−3
2
�=
�−3
2
(4)Replace the new y with ??????
−1
(�)
??????
−1
(�)=
�−3
2

11. EXAMPLE
Find the inverse of ??????(�)=3�+1.
Solution.
(1) Express the function in the form �=??????(�):
�=3�+1
(2) Interchange the x and y variables:
�=3�+1

12. (3) Solve for y in terms of x:
�=3�+1
−1(−3�=−�+1)
3�
3
=
�−1
3
�=
�−1
3
(4)Replace the new y with ??????
−1
(�)
??????
−1
(�)=
�−1
3

14. EXAMPLE
Find the inverse of ??????(�)=�
3
−2.
Solution.
(1) Express the function in the form �=??????(�):
�=�
3
−2
(2) Interchange the x and y variables:
�=�
3
−2

15. (3) Solve for y in terms of x:
�=�
3
−2
−1(−�
3
=−�−2)
3
�
3
=
3
�+2
�=
3
�+2
(4)Replace the new y with ??????
−1
(�)
??????
−1
(�)=
3
�+2

16. EXAMPLE

17. How did you determine the
inverse of a one-to-one
function?
How did you solve for the
inverse of a one-to-one
function?

18. ACTIVITY

19. THANK YOU
Mrs. Danica Jill Diao - Taguba