Let $A=\{1,2,3\}, B=\{4,5,6,7\}$ and let $f=\{(1,4),(2,5),(3,6)\}$ be a function from $A$ to $B$. State whether $f$ is one-one or not.

Question

LEELADHAR YADAV Asked Aug 29, 2023

45 views

1 Answer

RELATED DOUBTS

LEELADHAR YADAV Asked Aug 28, 2023

24 views

Let $A=\{1,2,3\}$ and $B=\{4,5,6\} f: A \rightarrow B$ is a function defined as $f(1)=4, f(2)=5, f(3)=6$. Write down $f^{\prime}$ as a set of ordered pairs.

LEELADHAR YADAV Asked Aug 28, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

24 Views

LEELADHAR YADAV Asked Sep 1, 2023

80 views

Show that the function $f$ in $A=R-\left\{\frac{2}{3}\right\}$ defined as $f(x)=\frac{4 x+3}{6 x-4}$ is one-one and onto. Hence find $f^{-1}$

LEELADHAR YADAV Asked Sep 1, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

80 Views

LEELADHAR YADAV Asked Aug 30, 2023

61 views

Let $A=R-\{3\}$ and $B=R-\{1\}$. Consider the function $f: A \rightarrow B$ defined by $f(x)=\left(\frac{x-2}{x-3}\right)$. Show that $f$ is oo one and onto and hence find $f^{-1}$.

LEELADHAR YADAV Asked Aug 30, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

61 Views

LEELADHAR YADAV Asked Aug 28, 2023

77 views

Let $f:(-1,1) \rightarrow B$, be a function defined by $f(x)=\tan ^{-1} \frac{2 x}{1-x^2}$, then $f$ is both one-one and onto when $B$ is the interval :

LEELADHAR YADAV Asked Aug 28, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

77 Views

LEELADHAR YADAV Asked Aug 27, 2023

119 views

Suppose $X$ and $Y$ are two sets and $f: X \rightarrow Y$ is a function. For a subset $A$ of $X$, define $f(A)$ to be the subset $\{f(a): a \in A\}$ of $Y$. For a subset $B$ of $Y$, define $f^{-1}(B)$ to be the subset $\{x \in X: f(x) \in B\}$ of $X$.

LEELADHAR YADAV Asked Aug 27, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

119 Views

LEELADHAR YADAV Asked Aug 28, 2023

65 views

Let $f$ be a function defined by $f(x)=(x-1)^2+1,(x \geq 1)$.

LEELADHAR YADAV Asked Aug 28, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

65 Views

LEELADHAR YADAV Asked Aug 28, 2023

11 views

Let $f: N \rightarrow Y$ be a function defined as $f(x)=4 x+3$, where $Y=\{y \in N: y=4 x+3$ for some $x \in N\}$. Show that $f$ is invertible. Find the inverse.

LEELADHAR YADAV Asked Aug 28, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

11 Views

LEELADHAR YADAV Asked Aug 28, 2023

54 views

If $g$ is the inverse of a function $f$ and $f^{\prime}(x)=\frac{1}{1+x^5}$, then $g^{\prime}(x)$ equal to:

LEELADHAR YADAV Asked Aug 28, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

54 Views

LEELADHAR YADAV Asked Aug 27, 2023

142 views

Let $f:(-1,1) \rightarrow \operatorname{IR}$ be such that $f(\cos 4 \theta)=\frac{2}{2-\sec ^2 \theta}$ for $\theta \in\left(0, \frac{\pi}{4}\right) \cup\left(\frac{\pi}{4}, \frac{\pi}{2}\right)$. Then the value $(s)$ of $f\left(\frac{1}{3}\right)$ is (are)

LEELADHAR YADAV Asked Aug 27, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

142 Views

LEELADHAR YADAV Asked Sep 3, 2023

112 views

Let $f(x)=x(2-x), 0 \leq x \leq 2$. If the definition of ' $f$ ' is extended over the set, $R-[0,2]$ by $f(x-2)=f(x)$, then prove that ' $f$ ' is a periodic function of period 2 .

LEELADHAR YADAV Asked Sep 3, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

112 Views

LEELADHAR YADAV Asked Aug 28, 2023

9 views

Let $f: R \rightarrow R$ be defined as $f(x)=x^4$. Show that $f$ is not one-one.

LEELADHAR YADAV Asked Aug 28, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

9 Views

LEELADHAR YADAV Asked Sep 3, 2023

91 views

Let $f(x)=A x^2+B x+C$, where $A, B, C$ are real numbers. Prove that if $f(x)$ is an integer whenever $x$ is integer, then the numbers $2 A, A+B$ and $C$ are all integers.

LEELADHAR YADAV Asked Sep 3, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

91 Views

LEELADHAR YADAV Asked Aug 28, 2023

49 views

Let $f: N \rightarrow Y$ be a function defined as $f(x)=4 x+3$ where $Y=\{y \in N: y=4 x+3$ for some $x \in N\}$. Its inverse is -

LEELADHAR YADAV Asked Aug 28, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

49 Views

LEELADHAR YADAV Asked Sep 2, 2023

43 views

Let $f(x)=\left(x^{12}-x^9+x^4-x+1\right)^{-1 / 2}$. The domain of the function is :

LEELADHAR YADAV Asked Sep 2, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

43 Views

Aayush Asked Jan 4

65 views

For the cell prepared from electrode A and B, electrode $A : \frac{ Cr _{2} O _{7}^{2-}}{ Cr ^{3+}}, E _{\text {red. }}^{0}=+1.33 V$ and electrode $B$ : $\frac{F_{e^{3+}}^{F e^{2+}}, E_{\text {red. }}^{0}}{}=0.77 V$, which of the following statement is not correct?

Aayush Asked Jan 4

by Aayush

1 Answer

0 Votes

65 Views

LEELADHAR YADAV Asked Aug 17, 2023

138 views

Let A={1,2,3,4,5,6} and * be an operation A defined by $a{ }^* b=r$, where r is the least non-negative remainder when the product a b is divided by k. Operation * is binary operation if k=

LEELADHAR YADAV Asked Aug 17, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

138 Views

thedablukumar Asked Jan 13, 2023

24 views

यदि $A=\{1,2,3\}, B=\{6,7,8\}$ तथा $f: A \rightarrow B$ एक फलन है, इस प्रकार कि $f(x)=x+5$, तो $f$ निम्नलिखित में से किस प्रकार का फलन है?

thedablukumar Asked Jan 13, 2023

by thedablukumar

1 Answer

0 Votes

24 Views

LEELADHAR YADAV Asked Sep 2, 2023

39 views

Find the values of ' $a$ ' in the domain of the definition of the function, $f(a)=\sqrt{2 a^2-a}$ for which the roots of the equation, $x^2+(a+1) x+(a-1)=0$ lie between $-2 \& 1$.

LEELADHAR YADAV Asked Sep 2, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

39 Views

LEELADHAR YADAV Asked Aug 28, 2023

81 views

If $\mathrm{f}$ be a greatest integer function and $\mathrm{g}$ be an absolute value function. Find the value of $\text { (log) }\left(\frac{-3}{2}\right)+(\text { gof })\left(\frac{4}{3}\right) \text {. }$

LEELADHAR YADAV Asked Aug 28, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

81 Views

LEELADHAR YADAV Asked Sep 3, 2023

354 views

It is given that $f(x)$ is a function defined on $N$, satisfying $f(1)=1$ and for any $x \in N$ $f(x+5) \geq f(x)+5 \quad \text { and } \quad f(x+1) \leq f(x)+1$ If $g(x)=f(x)+1-x$, then $g(2016)$ equals

LEELADHAR YADAV Asked Sep 3, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

354 Views

LEELADHAR YADAV Asked Aug 27, 2023

48 views

Let $f:[0,4 \pi] \rightarrow[0, \pi]$ be defined by $f(x)=\cos ^{-1}(\cos x)$. The number of points $x \in[0,4 \pi]$ satisfying the equation $f(x)=\frac{10-x}{10}$ is

LEELADHAR YADAV Asked Aug 27, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

48 Views

LEELADHAR YADAV Asked Aug 27, 2023

86 views

The function $f:[0,3] \rightarrow[1,29]$, defined by $f(x)=2 x^3-15 x^2+36 x+1$, is $(3,-1), 70]$ (A) one-one and onto

LEELADHAR YADAV Asked Aug 27, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

86 Views

LEELADHAR YADAV Asked Aug 27, 2023

73 views

The maximum value of the function $f(x)=2 x^3-15 x^2+36 x-48$ on the set $A=\left\{x \mid x^2+20 \leq 9 x\right\}$ is P-2, $(4,-1)$, 8 .

LEELADHAR YADAV Asked Aug 27, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

73 Views

LEELADHAR YADAV Asked Aug 28, 2023

42 views

The largest interval lying in $\left(\frac{-\pi}{2}, \frac{\pi}{2}\right)$ for which the function $f(x)=4^{-x^2}+\cos ^{-1}\left(\frac{x}{2}-1\right)+\log (\cos x)$ is defined, is

LEELADHAR YADAV Asked Aug 28, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

42 Views

LEELADHAR YADAV Asked Aug 28, 2023

22 views

Let $y=\left\{n^2: n \in N\right\}$ Consider $f: N \rightarrow y$ as $f(n)=n^2$. Show that $f$ is invertible. Find the inverse of $f$.

LEELADHAR YADAV Asked Aug 28, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

22 Views

Chandan Asked Sep 12, 2023

101 views

Check whether the relation R defined in the set {1,2,3,4,5,6} as R= {(a, b) : b=a+1} is reflexive, symmetric or transitive.

Chandan Asked Sep 12, 2023

by Chandan

1 Answer

0 Votes

101 Views

LEELADHAR YADAV Asked Sep 2, 2023

48 views

The domain of the function $f(x)=\sqrt{\frac{1}{(|x|-1) \cos ^{-1}(2 x+1) \cdot \tan 3 x}}$ is:

LEELADHAR YADAV Asked Sep 2, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

48 Views

LEELADHAR YADAV Asked Aug 27, 2023

77 views

Let $(x, y)$ be such that $\sin ^{-1}(a x)+\cos ^{-1}(y)+\cos ^{-1}(b x y)=\frac{\pi}{2}$

LEELADHAR YADAV Asked Aug 27, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

77 Views

LEELADHAR YADAV Asked Sep 1, 2023

69 views

If the fuction $f: R \rightarrow R$ be given by $f(x)=x^2+2$ and $g: R \rightarrow R$ be given by $g(x)=\frac{x}{x-1}, x \neq 1$, find fog and $g$ and hence find fog (2) and gof $(-3)$.

LEELADHAR YADAV Asked Sep 1, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

69 Views

LEELADHAR YADAV Asked Aug 11, 2023

93 views

Given a binary operation $: A \times A \rightarrow A$ with the identity element $e$ in $A$, an element $a \in A$ is said to be invertible with respect to the operation * if there exists an element $b$ in A such that $a^* b=e=b^* a$ and $b$ is called the inverse of $a$ and is denoted by ${a}^{-1}$.

LEELADHAR YADAV Asked Aug 11, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

93 Views

LEELADHAR YADAV Asked Sep 1, 2023

46 views

Find the domain of the function $f(x)=\sqrt{\frac{\log _{\frac{x}{2}}}{2} \log _2 \frac{2 x \quad 1}{3 x}}$

LEELADHAR YADAV Asked Sep 1, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

46 Views

LEELADHAR YADAV Asked Aug 29, 2023

37 views

Prove the following : $\tan ^{-1}\left(\frac{1}{3}\right)+\tan ^{-1}\left(\frac{1}{5}\right)+\tan ^{-1}\left(\frac{1}{7}\right)+\tan ^{-1}\left(\frac{1}{8}\right)=\frac{\pi}{4}$.

LEELADHAR YADAV Asked Aug 29, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

37 Views

LEELADHAR YADAV Asked Aug 27, 2023

77 views

If $\alpha=3 \sin ^{-1}\left(\frac{6}{11}\right)$ and $\beta=3 \cos ^{-1}\left(\frac{4}{9}\right)$, where the inverse trigonometric functions take only the principal values, then the correct option(s) is(are)

LEELADHAR YADAV Asked Aug 27, 2023

by LEELADHAR YADAV

0 Answers

0 Votes

77 Views

LEELADHAR YADAV Asked Aug 25, 2023

46 views

Let $f: A \rightarrow A$ where $A=\{x:-1 \leq x \leq 1\}$. Find whether the following functions are bijective.

LEELADHAR YADAV Asked Aug 25, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

46 Views

LEELADHAR YADAV Asked Aug 28, 2023

59 views

Let $\tan ^{-1} y=\tan ^{-1} x+\tan ^{-1}\left(\frac{2 x}{1-x^2}\right)$, where $|x|<\frac{1}{\sqrt{3}}$. Then a value of $y$ is

LEELADHAR YADAV Asked Aug 28, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

59 Views

ASK DOUBTS

Let $A=\{1,2,3\}, B=\{4,5,6,7\}$ and let $f=\{(1,4),(2,5),(3,6)\}$ be a function from $A$ to $B$. State whether $f$ is one-one or not.

0 Comments

Please log in or register to add a comment.

Please log in or register to answer this question.

1 Answer

0 Comments

Please log in or register to add a comment.

RELATED DOUBTS

CATEGORIES

POPULAR TAGS