Mathematics Crash Course JEE Main>Chapter 11 - Functions>Level 1>Q 7

MEDIUM

JEE Main

IMPORTANT

Earn 100

What is the range of the function $y = \frac{x^{2}}{1 + x^{2}},$ where $x \in R$ ?

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Important Questions on Functions

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 11 - Functions>Level 1>Q 8

If

f (x_{1}) - f (x_{2}) = f (\frac{x_{1} - x_{2}}{1 - x_{1} x_{2}})

for

x_{1}, x_{2} \in (- 1, 1)

, then what is

f (x)

equal to

?

EASY

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 11 - Functions>Level 1>Q 9

If for non-zero

x,

a f (x) + b f (\frac{1}{x}) = \frac{1}{x} - 5

, where

a \neq b,

then

f (2) =

MEDIUM

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 11 - Functions>Level 1>Q 10

f : R \to R, f (x) = \frac{\sin (π \{x\})}{x^{4} + 3 x^{2} + 7}

where

{*}

is a fractional function, then

MEDIUM

JEE Main

IMPORTANT

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

If

f : R \to S

is defined by

f (x) = 4 \sin x - 3 \cos x + 1

is an onto function, then what

S

is equal to ?

MEDIUM

JEE Main

IMPORTANT

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

If for two functions

g

and

f, g o f

is both injective and surjective. Which of the following is true?

MEDIUM

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,

MEDIUM

JEE Main

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?