Mathematics Crash Course JEE Main>Chapter 11 - Functions>Level 1>Q 25

EASY

JEE Main

IMPORTANT

Earn 100

If $f$ is a function defined on $(0, 1)$ by $f (x) = \max {x - [x], - x - [x]}$ , then $(f o f o f o f) (x)$ is equal to ([.] greatest integer function)

40% studentsanswered this correctly

Important Questions on Functions

MEDIUM

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 11 - Functions>Level 1>Q 26

Let

f : R - {3} \to R - {1}

be defined by

f (x) = \frac{x - 2}{x - 3}

. Let

g : R \to R

be given as

g (x) = 2 x - 3

. Then, the sum of all the values of

x

for which

f^{- 1} (x) + g^{- 1} (x) = \frac{13}{2}

is equal to

MEDIUM

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 11 - Functions>Level 2>Q 1

The domain of the function

f (x) = \log_{e} (sgn (9 - x^{2})) + \sqrt{[x]^{3} - 4 [x]}

(where

[\cdot]

represents the greatest integer function) is:

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 11 - Functions>Level 2>Q 2

If

f (x)

is continuous such that

|f (x)| \leq 1, \forall x \in R

and

g (x) = \frac{e^{f (x)} - e^{|f (x)|}}{e^{f (x)} + e^{|f (x)|}}

, then range of

g (x)

is:

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 11 - Functions>Level 2>Q 3

Let

f

be a function defined on

[- \frac{π}{2}, \frac{π}{2}]

b

f (x) = 3 \cos^{4} x - 6 \cos^{3} x - 6 \cos^{2} x - 3 .

Then, the range of

f (x)

is

MEDIUM

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 11 - Functions>Level 2>Q 4

Number of integer(s) in domain of function

f (x) = \log_{[x^{2}]} (4 - | x |) + \log_{2} {\sqrt{x}}

(where

[\cdot]

is G.I.F and

\{\cdot\}

is fractional part function of

x

), is:

MEDIUM

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 11 - Functions>Level 2>Q 5

Let

f

be a function with the following properties:
(i)

f (1) = 1

, and
(ii)

f (2 n) = n \times f (n) \cdot

for any positive integer

n

.
If the value of

f (2^{100}) = 2^{49 x y}

, then the digits

x

and

y

respectively?

MEDIUM

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 11 - Functions>Level 2>Q 6

Number of solutions of the equation

[y + [y]] = 2 c o s x

is, where

y = \frac{1}{3} [s i n x + [s i n x + [s i n x]]]

and

[\cdot]

denotes the greatest integer function.

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 11 - Functions>Level 2>Q 7

The number of solutions of the equation

[x] + 2 \{- x\} = 3 x,

is (where

[\cdot]

represents the greatest integer function and

\{x\}

denotes the fractional part of

x

):