Mathematics Crash Course JEE Main>Chapter 11 - Functions>Level 1>Q 12

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IMPORTANT

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If for two functions $g$ and $f, g o f$ is both injective and surjective. Which of the following is true?

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Important Questions on Functions

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 11 - Functions>Level 1>Q 13

Let

f : (1, \infty) \to [1, \infty)

be defined by

f (x) = \frac{x + 2}{x - 1} .

Then,

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 11 - Functions>Level 1>Q 14

f : R \to R

defined by

f (x) = \frac{1}{2} x | x | + \cos x + 1

is:

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 11 - Functions>Level 1>Q 15

Let

f, g : N \to N

such that

f (n + 1) = f (n) + f (1) \forall n \in N

and

g

be any arbitrary function. Which of the following statements is NOT true?

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 11 - Functions>Level 1>Q 16

Let

[x]

denote the greatest integer less than or equal to

x .

Then, the values of

x \in R

satisfying the equation

{[e^{x}]}^{2} + [e^{x} + 1] - 3 = 0

lie in the interval:

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 11 - Functions>Level 1>Q 17

Define

f : R \to R

by

f (x) = \max {x + 1, 1 - x, 2} .

Then

f

is

___

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 11 - Functions>Level 1>Q 18

If a function satisfies

f (x + 1) + f (x - 1) = \sqrt{2} f (x)

, then period of

f (x)

can be:

EASY

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 11 - Functions>Level 1>Q 19

If the graph of the function

f (x) = \frac{a^{x} - 1}{x^{n} (a^{x} + 1)}

is symmetrical about

y

-axis, then

n

equals

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 11 - Functions>Level 1>Q 20

Let

f

be a function with domain

[- 3, 5]

and let

g (x) = |3 x + 4|

, then the domain of

fog (x)

is