EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 9th April 2017>Q 51

HARD

JEE Main

IMPORTANT

Earn 100

The function $f : N \to I$ defined by $f (x) = x - 5 [\frac{x}{5}]$ , where $N$ is the set of natural numbers and $[x]$ denotes the greatest integer less than or equal to $x$ , 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 - 9th April 2016>Q 52

For

x \in R, x \neq 0, x \neq 1,

let

f_{0} (x) = \frac{1}{1 - x}

and

f_{n + 1} (x) = f_{0} (f_{n} (x)), n = 0, 1, 2, \dots . .

Then the value of

f_{100} (3) + f_{1} (\frac{2}{3}) + f_{2} (\frac{3}{2})

is equal to :

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 3rd April 2016>Q 53

If

f (x) + 2 f (\frac{1}{x}) = 3 x, x \neq 0,

and

S = \{x \in R : f (x) = f (- x)\}

, then

S

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 19th April 2014>Q 54

The function $f (x) = |sin 4 x| + |cos 2 x|,$ is a periodic function with a fundamental period

HARD

JEE Main

IMPORTANT

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

Let

f : R \to R

be defined by

f (x) = \frac{|x| - 1}{|x| + 1},

then

f

is

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 ______.