lesson plan

1. ANNEX 1B to DepEd Order No. 42, s. 2016
SESSION 4
I.OJECTIVES
A. Content Standards The learner demonstrates understanding of key concepts of inverse functions, exponential functions, and logarithmic functions.
B. Performance
Standards
The learner is able to apply the concepts of inverse functions, and logarithmic functions to formulate and solve real-life problems with precision
and accuracy.
C. Learning
Competencies
M11GM-Id-2
The learner determines the inverse of a one-to-one function.
At the end of the one hour session, the learners are able to:
a. Enumerates the properties of the inverse of a one-to-one function;
b. Determines the inverse of a one-to-one function;
c. Shows patience in determining the inverse of a one-to-one function.
II. CONTENT Inverse of One-to-One Functions
III. LEARNING RESOURCE
A. References
1. Teacher’s Guide
Pages
TG for SHS General Mathematics, pp. 69-75
2. Learner’s Materials
Pages
LM in General Mathematics, pp. 62-66
3. Textbook General Mathematics by Orlando Oronce Series 2016
4. Additional
Materials from
Learning Resource
Portal
Slide Decks on the Topic
B. Other Learning
Resource
General Mathematics, Diwa Publishing Series 2016
IV. PROCEDURES
A. Reviewing Previous
Lesson or
Presenting the New
Lesson
Recalling the table of values in the previous discussion. (referring to subtask 1)
Recall at the same time the definition of inverse of one-to-one function and the steps in finding the inverse of one-to-one function.
School: TUBALAN COMPREHENSIVE NATIONAL HIGH SCHOOL Grade Level & Section GRADE 11
Teacher: LESLIE VINE A. DELOSO Learning Area GENERAL MATHEMATICS
Teaching Dates & Time: Quarter 1 – week 4 day 3

2. B. Establishing a
Purpose for the
Lesson
Ask: Does the table still represent a function?
We should see that it can still represent a function because each x value is associated with only one y value.
Then consider the next table of values.
C. Presenting
Examples/Instances
of the New Lesson
Consider another table of values for another function.
Show the that the table does not represent a function because there are some y-values because here are some y-values that are
paired with more the one x-value.
For example, y =1 is paired with x = 1,2,3,4. Invert the values for x and y. Will the resulting table still represent a function?
The resulting table does not represent a function since x = 1 is paired with more than one y-value namely, 1,2,3 and 4.
Inverting’ Functions
The previous discussion shows that
 if the x- and y-values of a one-to-one function are interchanged, the result is a function, but
 if the x- and y-values of a function that is not one-to-one are inverted, the result is no longer a function.
D. Discussing New
Concepts and
Practicing New
Skills #1
Define the inverse of a one-to-one function.
Definition.
Let f be a one-to-one function with domain A and range B. Then the inverse of f, denoted 𝑓−1
, is a function with domain B and
range A defined by 𝑓−1 (𝑦) = 𝑥 if and only f(x) = y for any y in B.
A function has an inverse if and only if it is one-to-one. ‘Inverting’ the x-and y- values of a function results in a function if and
only if the original function is one-to-one.
E. Discussing New
Concepts and
Practicing New
Skills #2
To determine the inverse of a function from its equation.
The inverse of the function can be interpreted as the same function but in the opposite direction, that is, it is a function from the y-value
back to its corresponding x-value.
To find the inverse of a one-to-one function.
a) Write the function in the form y=f(x);
b) Interchange the x and y variables;

3. c) Solve for y in terms of x.
This is because we are interchanging the input and output values of a function.
Giving example.
1. Find the inverse of f(x) = 3x +1.
Solution. The equation of the function is y = 3x +1. Interchange the x and y variables: x =3y + 1.
Solve for y in terms of x:
Solution:
x = 3y + 1
x – 1 = 3y
𝑥−1
3
= 𝑦 ⟹ 𝑦 =
𝑥−1
3
Therefore, f (x) = 3x +1 is 𝑓−1
(x) =
𝑥−1
3
.
Ask the following questions to the class:
a) What is the inverse of the inverse?
b) What is f(𝑓−1
(𝑥))? How about 𝑓−1
(f(x))?
Have the class do these on the example above. The discuss the following properties that the class should have observed from the example
above.
Note: (Subtask 2) the following day.
F. Developing
Mastery (Leads to
Formative
Assessment)
Find the inverse of the following:
1. g(x) = 𝑥3
− 2
2. f(x) =
2𝑥+1
3𝑥−4
Solution:
1. The equation of the function is y = 𝑥3
− 2. Interchange the x and y variables: x = 𝑦3
− 2. Solve for y in terms of x:
x = 𝑦3
− 2
x + 2 = 𝑦3
√𝑥 + 2
3
= 𝑦 ⟹ 𝑦 √𝑥 + 2
3
The inverse of g(x) = 𝑦3
− 2 is 𝑔−1(𝑥) = √𝑥 + 2
3
.
2. The equation of the function is y =
2𝑥+1
3𝑥−4
. Interchange the x and y variables: x =
2𝑥+1
3𝑥−4
. Solve for y in terms of x:
x =
2𝑥+1
3𝑥−4
x(3y-4) = 2y + 1
3xy – 4x = 2y +1
3xy -2y = 4x + 1 (Place all terms with y on one side and those without y on the other side)
y (3x – 2) = 4x + 1
y =
4𝑥+1
3𝑥−2

4. Therefore, the inverse of f(x) is 𝑓−1(𝑥) =
4𝑥+1
3𝑥−2
.
G. Finding Practical
Applications of
Concepts and Skills
in Daily Living
Cite a real-life situation showing an inverse of one-to-one function.
1. To convert from degrees Fahrenheit to Kelvin, the function is ,where t is the temperature in Fahrenheit
(Kelvin is the SI unit of temperature). Find the inverse function converting the temperature in Kelvin to degrees Fahrenheit.
Solution. The equation of the function is . To maintain k and t as the respective temperatures in Kelvin and
Fahrenheit (and lessen confusion), let us not interchange the variables. We just solve for t in terms of k: ,
Therefore the inverse is with temperature in Kelvin.
2. Give 3 examples of situations that can be represented as a one-to-one function and two examples of situations that are not one-to-one.
Sample answer:
 vehicles to plate numbers
 movie tickets to seat numbers
 presidents or prime ministers to countries
 mayors to cities or towns
3. Choose a situation or scenario that can be represented as one-to-one function and explain why it is important that the function in the
scenario is one-to-one.
 A person must have only one tax Identification number (TIN) so that all the taxes he pays can be accurately recorded. If he has two
TINs, the BIR might think that he did not pay all his taxes if his payments are split between multiple TINs. If a single TIN has two
persons associated to it, then it would not be possible to ascertain which person is paying the proper taxes and which is not.
H. Making
Generalizations
and Abstractions
About the Lesson
Ask: Enumerate the properties of finding the inverse of one-to-one function.
How to find the inverse of a one-to-one function?
I. Evaluating Learning Find the inverse functions of the following one-to-one functions.
a) f(x) =
1
2
𝑥 + 4
b) f(x) = (𝑥 + 3)3
c) f(x) =
3
𝑥−4
d) f(x) =
𝑥+3
𝑥−3
e) f(x) =
2𝑥+1
4𝑥−1

5. Answer:
a) 𝑓−1
(x) = 2x – 8
b) 𝑓−1
(x) = √𝑥
3
– 3
c) 𝑓−1
(x) =
4𝑥+3
𝑥
d) 𝑓−1
(x) =
3𝑥+3
𝑥−1
e) 𝑓−1
(x) =
𝑥+1
4𝑥−2
J. Additional
Activities for
Application or
Remediation
V. REMARKS Worksheets can be given as an assignment
VI. REFLECTION
A. No. of Learners
who Earned 80% in
the Evaluation.
B. No. of Learners
Who Require
Additional
Activities for
Remediation Who
Scored Below 80%
C. Did the Remedial
Lesson Work? No.
of Learners Who
Have Caught Up
with the Lesson
D. No. Learners Who
Continue To
Require
Remediation
E. Which of My
Teaching Strategies
Worked Well? Why
Did These Work?
F. What Difficulties
Did I Encounter
Which My Principal

6. or Supervisor Can
Help Me Solve?
G. What Innovation or
Localized Materials
Did I Use/Discover
Which I Wish To
Share With Other
Teachers?
PREPARED BY:
LESLIE VINE A. DELOSO
SST – 1
OBSERVED BY:
GEORGE GARRIDO
MASTER TEACHER 1
CHECKED BY:
JOSIE R. DELA CRUZ
HEAD TEACHER