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

HARD

JEE Main

IMPORTANT

Earn 100

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 $x$ ):

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Important Questions on Functions

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 11 - Functions>Level 2>Q 8

Let

f : R^{+} \to \{- 1, 0, 1\}

be defined by

f (x) = sgn (x - x^{4} + x^{7} - x^{8} - 1)

where

sgn

denotes signum function. Then

f (x)

is.

MEDIUM

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 11 - Functions>Level 2>Q 9

If

f (x)

and

g (x)

are non-periodic functions, then

h (x) = f (g (x))

is:

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 11 - Functions>Level 2>Q 10

Which of the following functions is an odd function?

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JEE Main

IMPORTANT

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

The function $f (x) = \sin^{4} (x + \frac{π}{6}) + \cos^{4} (x + \frac{π}{6})$ is

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 11 - Functions>Level 2>Q 12

Let

G (x) = (\frac{1}{a^{x} - 1} + \frac{1}{2}) F (x),

where

a

is a positive real number not equal to

1

and

F (x)

is an odd function. Which of the following statements is true?

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 11 - Functions>Level 2>Q 13

f (x) = \sin x + \cos x, g (x) = x^{2} - 1

then

g (f (x))

is invertible if

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 11 - Functions>Level 2>Q 14

Let

f : X \to Y, f (x) = \sin x + \cos x + 2 \sqrt{2}

be invertible. Then,

X \to Y

is/are:

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 11 - Functions>Level 2>Q 15

Let

f : R \to R

and

g : R \to R

be two one-one and onto functions, such that they are the mirror images of each other about the line

y = a

. If

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

, then

h (x)

is