Recent Trends in PYQs
1. Number of Functions
2. Domain and Range
3. Functional Equation
4. Composite Functions
5. Inverse of Function
Question (JEE Main 2024)
Question (JEE Main 2023)
Definition of Functions
A = {1, 2, 3}
B = {a, b}
A x B = {(1, a), (1, b), (2, a) (2, b), (3, a), (3, b)}
AxB
Subset of A x B = Relations
Function Not function
Definition of Functions
Every element of A must have one and only one image in B
Function or NOT?
B AA B
a p a p
b q b q
c r c r
d s d s
A B
a p a p
b q b q
c r c r
d s s
d
t
Is RAMAYAN a Function?
Is Mahabharata a Function?
Arjun
Bhim
Yudhisthir Draupadi
Nakul
Sahadev
Domain, Codomain and Range
Domain =
A B
Codomain =
Range = a p
b q
c r
d s
Domain, Codomain and Range
Domain =
A B
Codomain =
Range = 1 1
-1 4
3 9
-3 16
Types of Functions
1. One-one and many-one
2. Onto and into
Types of Functions
B AA B
a p a p
b q b q
c r c r
d s d
A B
a p a p
b q b q
c r c r
d s s
d
t
Question (JEE Main 2024)
Question (JEE Main 2022)
Shortcut - Graphical Method
Horizontal line test
Vertical line test
HLT → To check whether the fn is one-one/many-one
VLT → to check whether it is fn or not
Examples
Alternate Names
One - one ↔ Injective
Onto ↔ Surjective
Injective + Surjective = Bijective
Number of Functions
CASE 1: n(A) = n(B)
Number of Functions
CASE 2: n(A) > n(B)
Number of Functions
CASE 3: n(A) < n(B)
Summary - Number of Functions
n(A) = a and n(B) = b
CASE Total onto one-one
n(A) = n(B) ba a! a!
n(A) > n(B) ba Grouping 0
n(A) < n(B) ba 0
Question (JEE Main 2024)
Question (JEE Advanced 2018)
Solution
Question (JEE Main 2023)
Solution
Question (JEE Main 2024)
Solution
Question (JEE Main 2023)
Solution
Domain of Functions
Question (JEE Main 2024)
Question (JEE Main 2024)
Range of Functions
Range of Functions (Type - 1)
Question (JEE Main 2024)
Range of Functions (Type - 2)
Question (JEE Main 2024)
Range of Functions (Type - 3)
Graph of Linear / Linear
Graph of Linear / Linear
Range of Functions (Type - 4)
Range of Functions (Type - 5)
Question (JEE Main 2023)
Question (JEE Advanced 2018)
Question (JEE Advanced 2018)
Question (JEE Advanced 2018)
Question (JEE Advanced 2018)
Question (JEE Advanced 2024)
Question (JEE Advanced 2024)
Question (JEE Advanced 2024)
Question (JEE Advanced 2024)
Functional Equations
1 f(x + y) = f(x) + f(y) ⇒ f(x) = kx
2 f(x + y) = f(x) . f(y) ⇒ f(x) = ax
3 f(xy) = f(x) + f(y) ⇒ f(x) = k lnx or f(x) =0
4 f(xy) = f(x) . f(y) ⇒ f(x) = xn
Question (JEE Advanced 2024)
Question (JEE Main 2024)
Question (JEE Main 2023)
Question (JEE Advanced 2020)
Composite Function
Question (JEE Main 2024)
Question (JEE Main 2024)
Question (JEE Main 2024)
Inverse of a Function
Question (JEE Main 2021)
Question (JEE Main 2023)
Inverse Trigonometric - Basic Properties
Question (JEE Advanced 2024)
Question (JEE Main 2024)
Inverse Trigonometric - Equations
Inverse Trigonometric - Equations
JEE 2024 JEE 2022 JEE 2023
Summation of Series
Question (JEE Main 2023)
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