EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 2 September 2020 Shift 2>Q 24

MEDIUM

JEE Main

IMPORTANT

Earn 100

Let $f : R \to R$ be a function which satisfies $f (x + y) = f (x) + f (y), \forall x, y \in R$ . If $f (1) = 2$ and $g (n) = \sum_{k = 1}^{(n - 1)} f (k),$ $n \in N$ then the value of $n$ , for which $g (n) = 20$ , is

50% studentsanswered this correctly

Important Questions on Functions

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 4 September 2020 Shift 1>Q 25

Let

[t]

denote the greatest integer

\leq t

. Then the equation in

x, {[x]}^{2} + 2 [x + 2] - 7 = 0

has :

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 5 September 2020 Shift 2>Q 26

Let

A = {a, b, c}

and

B = {1, 2, 3, 4} .

Then the number of elements in the set

C = {f : A \to B ∣ 2 \in f (A)

and

f

is not one-one

}

is

\dots

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 6 September 2020 Shift 2>Q 27

For a suitably chosen real constant

a

, let a function,

f : R - \{- a\} \to R

be defined by

f (x) = \frac{a - x}{a + x}

. Further supposed that for any real number

x \neq - a,

and

f (x) \neq - a, (fof) (x) = x

. Then

f (- \frac{1}{2})

is equal to :

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 7th January 2020 Shift 1>Q 28

If

g (x) = x^{2} + x - 1

and

(g o f) (x) = 4 x^{2} - 10 x + 5,

then

f (\frac{5}{4})

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 7th January 2020 Shift 1>Q 29

Let

S

be the set of points where the function

, f (x) = |2 - | x - 3 ||, x \in R,

is not differentiable. Then

\sum_{x \in S} f (f (x))

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 8th January 2020 Shift 1>Q 30

The inverse function of

f (x) = \frac{8^{2 x} - 8^{- 2 x}}{8^{2 x} + 8^{- 2 x}}, x \in (- 1, 1),

is __________.

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 8th January 2020 Shift 2>Q 31

Let

S

be the set of all functions

f : [0, 1] \to R

which are continuous on

[0, 1]

and differentiable on

(0, 1)

. Then for every

f

in

S

, there exists

c \in (0, 1)

depending on

f

, such that.

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 8th January 2020 Shift 2>Q 32

Let

f : (1, 3) \to R

be a function defined by

f (x) = \frac{x [x]}{1 + x^{2}},

where

[x]

denotes the greatest integer

\leq x .

Then the range of

f

is