Determines the inverse of
a one-to-one function
Activity 1:
Which is Which?
Activity 2:
Reversing Table
y = 2x – 1
Is this a Function?
Is this a One-to-One Function?
Activity 2:
Reversing Table
Let us invert the values for x and y.
Does this table still represent a Function?
Therefore, it is a One-to-one function.
Activity 2:
Reversing Table
Consider the next table.
Is this a Function?
Is this a One-to-One Function?
Activity 2:
Reversing Table
Does this table still represent a
Function?
Therefore, it is NOT a One-to-one
function.
“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.
Definition
Let f be a one-to-one function
with domain A and range B.
-1
Then the inverse of f, denoted f ,
is a function with domain B and
range A
Steps in finding the
Inverse Function
Step 1: Replace f(x) with y.
Step 2: Interchange the
x and y variables
Step 3: Solve for y.
Step 4: Replace y with f -1(x)
Example 1
Find the inverse of the function
𝑓 𝑥 = 3𝑥 + 1
Example 2
Find the inverse of the function
𝑓(𝑥)
= −4𝑥 + 6
Example 3
Find the inverse of the function
2𝑥 + 1
𝑓 𝑥 =
3𝑥 − 4
Activity 3: Math Relay
The class will be divided into three
groups. The group leader will assign
each member to a particular step in
solving the inverse of a one-to-one
function. And the first group to finish
will explain their answer.
Valuing:
Cite a real-life situation
where the concept of one-toone function or inverse
function applies?
Generalization
1.What do you mean by inverse
function?
2. Are all functions have their
inverse functions?
3. How to find the inverse of a
one-to-one function?
Assessment
Solve for the inverse function of the following oneto-one function.
1. 𝒇 𝒙 = −𝟓𝒙 + 𝟕
2. 𝒇 𝒙
𝟑𝒙−𝟐
=
𝟕𝒙+𝟏
3.f(x)=4x − 3
4.f(x)=2x + 6
5.f(x)=5x − 3
𝒙+𝟑
-1
a. f (x) =
𝟒
𝒙+𝟑
-1
b. f (x) =
𝟓
−𝒙+𝟕
-1
c. f (x) =
𝟓
𝒙
-1
d. f (x) = − 𝟑
𝟐
𝒙−𝟐
-1
e. f (x) =
𝟕𝒙 −𝟑
Have an advance study
on graphing inverse
function and identifying
its domain and range.
Any Questions ?