Ncert Solutions Maths class 12th

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New answer posted•a year ago

Ncert Solutions Maths class 12th Relations and Functions

Let $f = {(1, 2), (3, 5), (4, 1)}$ and $g = {(2, 3), (5, 1), (1, 3)}$ . Then $g \circ f =$ and $f \circ g =__.$

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 Fill in the Blanks Type Question as classified in NCERT Exemplar

Sol:

$\begin{array}{l} \end{array} G i v e n t h a t, f = {(1, 2), (3, 5), (4, 1)} a n d g = {(2, 3), (5, 1), (1, 3)}$

$g o f (1) = g {f (1)} = g (2) = 3$

$g o f (3) = g {f (3)} = g (5) = 1$

$g o f (4) = g {f (4)} = g (1) = 3$

$\begin{array}{l} ∴ g o f = {(1, 3), (3, 1), (4, 3)} \end{array}$

$\begin{array}{l} \end{array} f o g (2) = f {g (2)} = f (3) = 5$

$f o g (5) = f {g (5)} = f (1) = 2$

$f o g (1) = f {g (1)} = f (3) = 5$

$∴ f o g = {(2, 5), (5, 2), (1, 5)}$

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New answer posted•a year ago

Ncert Solutions Maths class 12th Relations and Functions

Let the relation $R$ be defined on the set $A = {1, 2, 3, 4, 5}$ by $R = {(a, b) : ∣ a^{2} - b^{2} ∣ < 8}$ . Then $R$ is given by ________

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 Fill in the Blanks Type Question as classified in NCERT Exemplar

Sol:

Upvote

New answer posted•a year ago

Ncert Solutions Maths class 12th Relations and Functions

Let the relation $R$ be defined in $ℕ$ by $a R b$ if $2 a + 3 b = 30$ . Then $R =________.$

2 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:

Upvote

New answer posted•a year ago

Ncert Solutions Maths class 12th Relations and Functions

Let $f : R \to R$ be given by $f (x) = t a n x$ . Then $f^{- 1} (1)$ is

(A) $\frac{π}{4}$

(B) ${n π + \frac{π}{4} : n \in ℤ}$

(C) Does not exist

(D) None of these

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 Objective Type Question as classified in NCERT Exemplar

Sol:

$\begin{array}{l} G i v e n t h a t f (x) = t a n x \\ L e t f (x) = y = t a n x \Rightarrow x = t a n^{- 1} y \\ \Rightarrow f^{- 1} (x) = t a n^{- 1} (x) \\ \Rightarrow f^{- 1} (1) = t a n^{- 1} (1) \\ \Rightarrow f^{- 1} (1) = t a n^{- 1} [t a n (\frac{π}{4})] = \frac{π}{4} \\ H e n c e, t h e c o r r e c t a n s w e r i s (a) . \end{array}$

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New answer posted•a year ago

Ncert Solutions Maths class 12th Relations and Functions

Let $f : R \to R$ be defined by:

Then $f (- 1) + f (2) + f (4)$ is

(A) 9

(B) 14

(C) 5

(D) None of these

10 Views|Posted a year ago

Asked by Alok Kumar Singh

Answered by

Alok Kumar Singh | Contributor-Level 10

a year ago

This is a Objective Type Question as classified in NCERT Exemplar

Sol:

$\begin{array}{l} G i v e n t h a t : \\ f (x) = {\begin{cases} 2 x : x > 3 \\ x^{2} : 1 < x \leq 3 \\ 3 x : x \leq 1 \end{cases}} \\ ∴ f (- 1) + f (2) + f (4) = 3 (- 1) + {(2)}^{2} + 2 (4) = - 3 + 4 + 8 = 9 \\ H e n c e, t h e c o r r e c t a n s w e r i s (a) . \end{array}$

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New answer posted•a year ago

Ncert Solutions Maths class 12th Relations and Functions

Let $f : N \to R$ be the function defined by $f (x) = \frac{2 x - 1}{2}$ and $g : Q \to R$ be another function defined by $g (x) = x + 2$ . Then $($ $(g \circ f)$
$\frac{3}{2}$ is

(A) 1

(B) 1

(C) $\frac{7}{2}$

(D) None of these

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 Objective Type Question as classified in NCERT Exemplar

Sol:

$\begin{array}{l} H e r e, f (x) = \frac{2 x - 1}{2} a n d g (x) = x + 2 \\ ∴ g o f (x) = g [f (x)] \\ = f (x) + 2 \\ = \frac{2 x - 1}{2} + 2 = \frac{2 x + 3}{2} \\ g o f (\frac{3}{2}) = \frac{2 \times \frac{3}{2} + 3}{2} = 3 \\ H e n c e, t h e c o r r e c t a n s w e r i s (d) . \end{array}$

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New answer posted•a year ago

Ncert Solutions Maths class 12th Relations and Functions

Let $f : [2, \infty) \to R$ be the function defined by $f (x) = x^{2} - 4 x + 5$ . Then the range of $f$ is

(A) $?$

(B) $[1, \infty)$

(C) $[4, \infty)$

(D) $[5, \infty)$

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 Objective Type Question as classified in NCERT Exemplar

Sol:

Upvote

New answer posted•a year ago

Ncert Solutions Maths class 12th Relations and Functions

Let $f : [0, 1] \to [0, 1]$ be defined by $f (x) = {\begin{matrix} x, & if x is rational \\ 1 - x, & if x is irrational \end{matrix}$

Then $(f \circ f) x i s$

(A) Constant

(B) $1 + x$

(C) $x$

(D) None of these

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 Objective Type Question as classified in NCERT Exemplar

Sol:

$\begin{array}{l} G i v e n t h a t f : [0, 1] \to [0, 1] \\ ∴ f = f^{- 1} \\ S o, (f o f) x = x (i d e n t i t y e l e m e n t) \\ H e n c e, ? ? ? t h e c o r r e c t a n s w e r i s (c) . \end{array}$

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New answer posted•a year ago

Ncert Solutions Maths class 12th Relations and Functions

Let $f : R - {\frac{3}{5}} \to R$ be defined by $f (x) = \frac{3 x + 2}{5 x - 3}$ . Then

(A) $f^{- 1} (x) = f (x)$

(B) $f^{- 1} (x) = - f (x)$

(C) ( $f \circ f$ )x=-x

(D) $f^{- 1} (x) = \frac{1}{19} f (x)$

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 Objective Type Question as classified in NCERT Exemplar

Sol:

$\begin{array}{l} G i v e n t h a t f (x) = \frac{3 x + 2}{5 x - 3} \forall x \neq \frac{3}{5} \\ L e t y = \frac{3 x + 2}{5 x - 3} \\ \Rightarrow y (5 x - 3) = 3 x + 2 \\ \Rightarrow 5 x y - 3 y = 3 x + 2 \\ \Rightarrow 5 x y - 3 x = 2 + 3 y \\ \Rightarrow x (5 y - 3) = 2 + 3 y \\ \Rightarrow x = \frac{3 y + 2}{5 y - 3} \\ \Rightarrow f^{- 1} (x) = \frac{3 x + 2}{5 x - 3} \\ \Rightarrow f^{- 1} (x) = f (x) \\ H e n c e, t h e c o r r e c t a n s w e r i s (a) . \end{array}$