Mathematics Crash Course JEE Main>Chapter 11 - Functions>Level 2>Q 18

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If the function $f : [1, \infty) \to [1, \infty)$ is defined by $f (x) = 2^{x (x - 1)}$ , then $f^{- 1} (x)$ is

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Important Questions on Functions

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Mathematics Crash Course JEE Main>Chapter 11 - Functions>Level 2>Q 19

Let

f : [- \frac{π}{3}, \frac{2 π}{3}] \to [0, 4]

be a function defined as

f (x) = \sqrt{3} \sin x - \cos x + 2 .

Then

f^{- 1} (x)

is given by

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Mathematics Crash Course JEE Main>Chapter 11 - Functions>Level 2>Q 20

If

f (x) = \{\begin{cases} - x + 1, & x \leq 0 \\ - {(x - 1)}^{2}, & x \geq 1 \end{cases}

then the number of solution(s) of

f (x) - f^{- 1} (x) = 0

is

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Mathematics Crash Course JEE Main>Chapter 11 - Functions>Level 3>Q 1

If

f (x) = x^{2} + x + \frac{3}{4}

and

g (x) = x^{2} + a x + 1

be two real functions, then the range of

a

for which

g (f (x)) = 0

has no real solution, is

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

A function

f

from integers to integers is defined as

f (x) = \{\begin{matrix} n + 3, & n \in o d d \\ \frac{n}{2}, & n \in even \end{matrix}

suppose

k \in

odd and

f (f (f (k))) = 27

, then the sum of digits of

k

, is:

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

For any real number

x,

let

[x]

denote the integer part of

x; {x}

be the fractional part of

x .

(\{x\} = x - [x])

. Let

A

denote the set of all real numbers

x

satisfying

\{x\} = \frac{x + [x] + [x + (\frac{1}{2})]}{20}

. If

S

is the sum of all numbers in

A,

find

[S]

.

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Mathematics Crash Course JEE Main>Chapter 11 - Functions>Level 3>Q 4

The period of the function

c^{\{\sin^{2} x + \sin^{2} (x + \frac{π}{3}) + \cos x \cos (x + \frac{π}{3})\}}

is (where

c

is constant)

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Mathematics Crash Course JEE Main>Chapter 11 - Functions>Level 3>Q 5

Let

f

and

g

be functions defined by

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

and

g (x) = x^{2} + 1, x \in R .

Then,

g o f

is

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Mathematics Crash Course JEE Main>Chapter 11 - Functions>Level 3>Q 6

If

f (x)

and

g (x)

are periodic functions with periods

7

and

11,

respectively. Then, the period of

F (x) = f (x) \cdot g (\frac{x}{5}) + g (x) \cdot f (\frac{x}{3})

is