Ncert Solutions Maths class 12th

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New answer posted•a year ago

Ncert Solutions Maths class 12th Relations and Functions

The composition of functions is associative.

6 Views|Posted a year ago

Asked by Alok Kumar Singh

Answered by

Alok Kumar Singh | Contributor-Level 10

a year ago

This is a True or False Type Question as classified in NCERT Exemplar

Sol:

$\begin{array}{l} L e t f (x) = 2 x, g (x) = x - 1 a n d h (x) = 2 x + 3 \\ f o {g o h (x)} = f o {g (2 x + 3)} \\ = f (2 x + 3 - 1) = f (2 x + 2) = 2 (2 x + 2) = 4 x + 4 \\ a n d (f o g) o h (x) = (f o g) {h (x)} \\ = f o g (2 x + 3) \\ = f (2 x + 3 - 1) = f (2 x + 2) = 2 (2 x + 2) = 4 x + 4 \\ ∴ f o {g o h (x)} = (f o g) o h (x) = 4 x + 4 \\ H e n c e, t h e s t a t e m e n t i s T r u e . \end{array}$

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New answer posted•a year ago

Ncert Solutions Maths class 12th Relations and Functions

The composition of functions is commutative.

4 Views|Posted a year ago

Asked by Alok Kumar Singh

Answered by

Alok Kumar Singh | Contributor-Level 10

a year ago

This is a True or False Type Question as classified in NCERT Exemplar

Sol:

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New answer posted•a year ago

Ncert Solutions Maths class 12th Relations and Functions

The relation $R$ on the set $A = {1, 2, 3}$ defined as $R = {(1, 1), (1, 2), (2, 1), (3, 3)}$ is reflexive, symmetric, and transitive.

9 Views|Posted a year ago

Asked by Alok Kumar Singh

Answered by

Alok Kumar Singh | Contributor-Level 10

a year ago

This is a True or False Type Question as classified in NCERT Exemplar

Sol:

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New answer posted•a year ago

Ncert Solutions Maths class 12th Relations and Functions

Let $A = {0, 1}$ and $N$ be the set of natural numbers. Then the mapping $f : N \to A$ defined by $f (2 n - 1) = 0, f (2 n) = 1, \forall n \in N$ , is onto.

8 Views|Posted a year ago

Asked by Alok Kumar Singh

Answered by

Alok Kumar Singh | Contributor-Level 10

a year ago

This is a True or False Type Question as classified in NCERT Exemplar

Sol:

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New answer posted•a year ago

Ncert Solutions Maths class 12th Relations and Functions

An integer $m$ is said to be related to another integer $n$ if $m$ is a integral multiple of $n$ . This relation in $Z$ is reflexive, symmetric, and transitive.

3 Views|Posted a year ago

Asked by Alok Kumar Singh

Answered by

Alok Kumar Singh | Contributor-Level 10

a year ago

This is a True or False Type Question as classified in NCERT Exemplar

Sol:

$\begin{array}{l} H e r e, m = k n (w h e r e k i s a n i n t e g e r) \\ I f k = 1 m = n, s o z i s r e f l e x i v e . \\ C l e a r l y z i s n o t s y m m e t r i c b u t z i s t r a n s i t i v e . \\ H e n c e, t h e s t a t e m e n t i s f a l s e . \end{array}$

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New answer posted•a year ago

Ncert Solutions Maths class 12th Relations and Functions

Every relation which is symmetric and transitive is also reflexive.

5 Views|Posted a year ago

Asked by Alok Kumar Singh

Answered by

Alok Kumar Singh | Contributor-Level 10

a year ago

This is a True or False Type Question as classified in NCERT Exemplar

Sol:

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New answer posted•a year ago

Ncert Solutions Maths class 12th Relations and Functions

Let $f : R \to R$ be the function defined by $f (x) = s i n (3 x + 2), \forall x \in R$ . Then $f$ is invertible.

5 Views|Posted a year ago

Asked by Alok Kumar Singh

Answered by

Alok Kumar Singh | Contributor-Level 10

a year ago

This is a True or False Type Question as classified in NCERT Exemplar

Sol:

$\begin{array}{l} G i v e n t h a t, f (x) = s i n (3 x + 2), \forall x \in R \\ f (x) i s n o t o n e - o n e f u n c t i o n . \\ H e n c e, t h e s t a t e m e n t i s f a l s e . \end{array}$

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New answer posted•a year ago

Ncert Solutions Maths class 12th Relations and Functions

State True or False for the statements in each of the Exercises 6 to 14:

Let $R = {(3, 1), (1, 3), (3, 3)}$ be a relation defined on the set $A = {1, 2, 3}$ . Then $R$ is symmetric, transitive but not reflexive.

5 Views|Posted a year ago

Asked by Alok Kumar Singh

Answered by

Alok Kumar Singh | Contributor-Level 10

a year ago

This is a True or False Type Question as classified in NCERT Exemplar

Sol:

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New answer posted•a year ago

Ncert Solutions Maths class 12th Relations and Functions

If $f (x) = (4 - {(x - 7)}^{3}}$ , then $f^{- 1} (x) =________.$

7 Views|Posted a year ago

Asked by Alok Kumar Singh

Answered by

Alok Kumar Singh | Contributor-Level 10

a year ago

This is a Fill in the Blanks Type Question as classified in NCERT Exemplar

Sol:

$\begin{array}{l} f (x) = [4 - {(x - 7)}^{3}] \\ L e t y = [4 - {(x - 7)}^{3}] \\ \Rightarrow {(x - 7)}^{3} = 4 - y \\ \Rightarrow x - 7 = {(4 - y)}^{\frac{1}{3}} \Rightarrow x = {(4 - y)}^{\frac{1}{3}} + 7 \\ H e n c e, f^{- 1} (x) = {(4 - y)}^{\frac{1}{3}} + 7 \end{array}$