EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 19th April 2014>Q 55

HARD

JEE Main

IMPORTANT

Earn 100

Let $f : R \to R$ be defined by $f (x) = \frac{|x| - 1}{|x| + 1},$ then $f$ is

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Important Questions on Functions

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 6th April 2014>Q 56

If

a \in R

and the equation

- 3 (x - [x])^{2} + 2 (x - [x]) + a^{2} = 0

(where

[x]

denotes the greatest integer

\leq

x

) has no integral solution, then all possible values of

a

lie in the interval

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 24 June 2022 Shift 1>Q 57

The domain of

f (x) = \frac{\cos^{- 1} (\frac{x^{2} - 5 x + 6}{x^{2} - 9})}{\log (x^{2} - 3 x + 2)}

is

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 25 June 2022 Shift 1>Q 58

Let

f : N \to R

be a function such that

f (x + y) = 2 f (x) f (y)

for natural numbers

x

and

y

. If

f (1) = 2

, then the value of

α

for which

\sum_{k = 1}^{10} f (α + k) = \frac{512}{3} (2^{20} - 1)

holds, is

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 25 June 2022 Shift 1>Q 59

Let

f : R \to R

be a function defined by

f (x) = {(2 (1 - \frac{x^{25}}{2}) (2 + x^{25}))}^{\frac{1}{50}}

. If the function

g (x) = f (f (f (x))) + f (f (x))

, then the greatest integer less than or equal to

g (1)

is ______.

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 26 June 2022 Shift 2>Q 60

Let

f : ℝ \to ℝ

be defined as

f (x) = x - 1

and

g : R \to \{1, - 1\} \to ℝ

be defined as

g (x) = \frac{x^{2}}{x^{2} - 1}

. Then the function

f o g

is:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 26 June 2022 Shift 2>Q 61

Let

f : ℝ \to ℝ

satisfy

f (x + y) = 2^{x} f (y) + 4^{y} (f (x), \forall x

,

y \in ℝ

. If

f (2) = 3

, then

14 \cdot \frac{f^{'} (4)}{f^{'} (2)}

is equal to _____.

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 26 June 2022 Shift 1>Q 62

Let

f (x) = \frac{x - 1}{x + 1}, x \in R - {0, - 1, 1)

. If

f^{n + 1} (x) = f (f^{n} (x))

for all

n \in N

, then

f^{6} (6) + f^{7} (7)

is equal to

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 27 June 2022 Shift 1>Q 63

Let

f : R \to R

be a function defined

f (x) = \frac{2 e^{2 x}}{e^{2 x} + e}

. Then

f (\frac{1}{100}) + f (\frac{2}{100}) + f (\frac{3}{100}) + \dots + f (\frac{99}{100})

is equal to ______.