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Chapter name 7th Jan-I
7th Jan-II
8th Jan-I
8th Jan-II
9th Jan-I
9th Jan-II
Sets, Relation & Functions 1 0 1 1 1 0
JEE MAIN 2020
Chapter name
9th jan(I)
9th jan(II)
10th jan(I)
10th jan(II)
11th jan(I)
11th jan(II)
12th jan(I)
12th jan(II)
Sets, Relation & Functions
2 2 0 2 1 1 2 1
JEE MAIN 2019
JEE MAIN PAST YEARS CHAPTERWISE WEIGHTAGE
JEE MAIN 2019
Chapter name
8th Apr(I)
8th Apr(II)
9th April(I)
9th April(II)
10th April(I)
10th April(II)
12th Apr(I)
12th April(II)
Sets, Relation & Functions
1 2 0 2 2 1 1 0
Chapter name 2018 2017 2016 2015
Sets, Relation & Functions 1 2 2 0
JEE MAIN PAST YEARS CHAPTERWISE WEIGHTAGE
Definition of a FunctionLet A and B be two non empty sets.A function from A to B i.e. f : A ⟶ B is a relation such that(a) all the elements of A are related to the elements of B and(b) no element of A is related to more than one element of B
Both are relations of course from A to B.
A B
f
A B
f
Rules of finding domain1
expression , then expression ≠ 01.
Expression√ , then Expression ≥ 02.
f(x)4. Domain is D1
g(x) Domain is D2
Domain is D1 ∩ D2f(x) ± g(x)
loga x3. , then x > 0 and a > 0 and a ≠ 1
DOMAIN OF A FUNCTION
RANGE OF A FUNCTION
y = f (x)
x = g (y)
Now, values of y for which g (y) i.e. x is defined is the required range
Rules of finding range
Say we need to find range of y = f (x)
Try to express it in following form
Consider
EVEN – ODD FUNCTION
A function f(x) is said to be even function; if f(– x) = f(x) ∀ x
Graph of an even function is symmetric about y – axis
A function f(x) is said to odd; if f(– x) = – f(x) ∀ x.
ONE –ONE AND MANY ONE FUNCTIONS
A function f:A → B is said to be one-one or injectiveif all elements of A have different images in B
Otherwise it is called many one function.
Mathematicallyif f (a) = f (b) ⇒ a = bthen f (x) is 1-1 (or injective)
● A function f(x) is said to be periodic function, if there exists a positive real number such that .
● Least such value of ‘T’ is called Fundamental Period of y = f(x).● Graph of periodic function repeats at fixed length of interval.
Methods to find Period
(1) If period of f(x) is T then period of y = kf (ax + b) + c is
(2) If period of f(x) is T1 and period of g(x) is T2 then LCM (T1, T2) is period
of f(x) + g(x). [It need not be fundamental period].
Periodic Function
● A function f(x) is said to be periodic function, if there exists a positive real number such that .
● Least such value of ‘T’ is called Fundamental Period of y = f(x).● Graph of periodic function repeats at fixed length of interval.
MODULUS FUNCTION
–a a
a
y = x
y = –x
Properties
1) a ≤ | a |
2) | ab | = | a | | b |
3) | a + b | ≤ | a | + | b |
If a > 0; then equality holds
4) | a – b | ≥ | || a | – | b |3 and 4 are called triangle inequalities
In 3 and 4, equality holds if ab ≥ 0
GREATEST INTEGER FUNCTION 321
0–3 –2 –1 1 2 3
–2–1
–3
Domain = Set of all real numbers
Range = Set of integers
Properties
1) [x] + [–x] =0 ; x ∈ Z
–1 ; x ∉ Z
2) [x + k] [x] + k, for k∈ Z =
[kx] ≠ k[x]
Graph
–2
–1
0 1 2 3
1
Domain : Set of all real numbers
Range : [ 0, 1 )
x + 2
x + 1 x x – 1
x – 2 { x } = x – [ x ]
x + 1 ; –1≤ x < 0
x ; 0≤ x < 1x – 1 ; 1≤ x < 2
Fractional Part Function
EXPONENTIAL FUNCTION
y = ax
a > 1 0 < a < 1
Increasing function Decreasing function
a > 0 ; a ≠ 1
If x is increasing Then y is increasing
If x is increasing Then y is decreasing
LOGARITHMIC FUNCTION
y = logax
log a b = c if b = ac
log28 = 3
log5625 = 4
(23 = 8)
(54= 625)
y = logax ; a > 0 ; a ≠ 1
1
1
Increasing function
Decreasingfunction
a > 1
0 < a < 1
Both have range: all real
Onto and into functions
A function f(x) from A to B is said to be onto or surjectivefunction if every element of B is image of some element of A.
i.e. Range of f(x) = Co – domain of f(x)
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Q1. If g(x) = x2 + x -1 and (gof)(x) = 4x2 - 10x + 5, then is equal to :
7th Jan 2020- Shift I
A
B
D
C
JEE MAIN Functions: Super JEE Revision
Q1. If g(x) = x2 + x -1 and (gof)(x) = 4x2 - 10x + 5, then is equal to :
7th Jan 2020- Shift I
A
B
D
C
JEE MAIN Functions: Super JEE Revision
Q2. The inverse function of , x (-1, 1) , is
7th Jan 2020- Shift II
A
B
D
C
JEE MAIN Functions: Super JEE Revision
Q2. The inverse function of , x (-1, 1) , is
7th Jan 2020- Shift II
A
B
D
C
JEE MAIN Functions: Super JEE Revision
A B
DC
Q5. If the function f:R-{1,-1}→A defined by , , is surjective, then A is equal to :
R-[-1,0) R-(-1,0)
R-{-1} [0,∞]
JEE-Main 2019, 9th April -I
JEE MAIN Functions: Super JEE Revision
A B
DC
Q5. If the function f:R-{1,-1}→A defined by , , is surjective, then A is equal to :
R-[-1,0) R-(-1,0)
R-{-1} [0,∞]
JEE-Main 2019, 9th April -I
JEE MAIN Functions: Super JEE Revision
A
Q7. The function
B
D
C
invertible.
injective but not surjective.
surjective but not injective.
neither injective nor surjective.
JEE (Main) 2017
JEE MAIN Functions: Super JEE Revision
A
Q7. The function
B
D
C
invertible.
injective but not surjective.
surjective but not injective.
neither injective nor surjective.
JEE (Main) 2017
JEE MAIN Functions: Super JEE Revision
A
B
Q8. If 𝛼 is a real number such that 𝛼
C
D
JEE-Main 2019, 10th April -II
JEE MAIN Functions: Super JEE Revision
A B
Q8. If 𝛼 is a real number such that 𝛼
C DJEE-Main 2019, 10th April -II
JEE MAIN Functions: Super JEE Revision
Q10. Let f : R+ ⟶ R be a function which satisfies then for f (1) =3, f(x) is equal to:
A
B
(2x-1)/x
(x+1)/x
D
C
(2x+1)/x
-(2x+1)/x
JEE MAIN Functions: Super JEE Revision
Q10. Let f : R+ ⟶ R be a function which satisfies then for f(1)=3, f(x) is equal to:
A
B
(2x-1)/x
(x+1)/x
D
C
(2x+1)/x
-(2x+1)/x
JEE MAIN Functions: Super JEE Revision
Homework Questions
A
B
D
C
Q1. Let f : (1,3) ⟶ R be a function defined by , where
[x] denotes the greatest integer ≤ x. Then the range of f is :
Homework Questions
A
Q2. Let f (x) = ax (a > 0) be written as f ( x ) = f1 ( x ) + f2 ( x ) , where f1 ( x ) is an even function and f2 ( x ) is an odd function. Then f1 ( x + y ) + f1( x - y) equals
B
D
C 2f1 ( x + y ) f2( x - y)
2f1 ( x + y ) f1( x - y)
2f1 ( x ) f2 ( y )
2f1 ( x ) f1 ( y )
Homework QuestionsQ3. If g is the inverse of a function f and f’(x) = , then g’(x) is equal to
A
B
D
C
A
B
D
C
Q1. Let f : (1,3) ⟶ R be a function defined by , where
[x] denotes the greatest integer ≤ x. Then the range of f is :
Solution of Homework Questions
A
B
D
C
Q1. Let f : (1,3) ⟶ R be a function defined by , where
[x] denotes the greatest integer ≤ x. Then the range of f is :
Solution of Homework Questions
A
Q2. Let f (x) = ax (a > 0) be written as f ( x ) = f1 ( x ) + f2 ( x ) , where f1 ( x ) is an even function and f2 ( x ) is an odd function. Then f1 ( x + y ) + f1( x - y) equals
B
D
C 2f1 ( x + y ) f2( x - y)
2f1 ( x + y ) f1( x - y)
2f1 ( x ) f2 ( y )
2f1 ( x ) f1 ( y )
Solution of Homework Questions
A
Q2. Let f (x) = ax (a > 0) be written as f ( x ) = f1 ( x ) + f2 ( x ) , where f1 ( x ) is an even function and f2 ( x ) is an odd function. Then f1 ( x + y ) + f1( x - y) equals
B
D
C 2f1 ( x + y ) f2( x - y)
2f1 ( x + y ) f1( x - y)
2f1 ( x ) f2 ( y )
2f1 ( x ) f1 ( y )
Solution of Homework Questions
Q3. If g is the inverse of a function f and f’(x) = , then g’(x) is equal to
A
B
D
C
Solution of Homework Questions