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

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IMPORTANT

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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:

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Important Questions on Functions

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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

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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:

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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?

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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.

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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

):

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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.

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

Which of the following functions is an odd function?