RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 1 - Relations and Functions>EXERCISE>Q 3

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12th West Bengal Board

IMPORTANT

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For the set of natural numbers $N$ , the function $f : N \to N$ defined by $f (x) = 2 x$ , $\forall x \in ℕ,$ is

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Important Questions on Relations and Functions

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12th West Bengal Board

IMPORTANT

RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 1 - Relations and Functions>EXERCISE>Q 3

For the set of all real numbers

R

, the function

f : R \to R

defined by

f (x) = x^{2}

,

\forall x \in R,

is

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12th West Bengal Board

IMPORTANT

RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 1 - Relations and Functions>EXERCISE>Q 3

For a finite set

A

of

n

elements, the number of functions from

A

to

A

is

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IMPORTANT

RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 1 - Relations and Functions>EXERCISE>Q 3

Let

A

be a finite set of

n

elements. Then the number of injective functions defined from

A

into

A

is

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12th West Bengal Board

IMPORTANT

RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 1 - Relations and Functions>EXERCISE>Q 3

Let

A

and

B

be two sets containing

3

and

4

elements respectively. Then the number of bijective mappings from the set

A

onto the set

B

is

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12th West Bengal Board

IMPORTANT

RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 1 - Relations and Functions>EXERCISE>Q 3

If, for the set of all real number

ℝ

,

f : ℝ \to ℝ

is a function defined by

f (x) = x^{2} - 3 x + 4, \forall x \in ℝ

, then

f^{- 1} ({2}) =

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12th West Bengal Board

IMPORTANT

RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 1 - Relations and Functions>EXERCISE>Q 3

For two functions

f : ℝ \to ℝ and g : ℝ \to ℝ

defined by

f (x) = \sin x and g (x) = x^{2}, \forall x \in ℝ, (f \circ g) (x) =

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12th West Bengal Board

IMPORTANT

RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 1 - Relations and Functions>EXERCISE>Q 3

f : [0, 1] \to [0, 1]

is a function defined by

f (x) = \{\begin{cases} x, when x is rational \\ 1 - x, when x is irrational \end{cases}

. Then,

f \circ f (x) =

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12th West Bengal Board

IMPORTANT

RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 1 - Relations and Functions>EXERCISE>Q 3

For the functions

f : ℝ \to ℝ

, where

f (x) = 5 - x^{2}

and

g : ℝ \to ℝ

, where

g (x) = 3 x - 4

, the value of

f \circ g (- 1)

is