Codomain

Q. Let $f:N\to N$ be a function such that $f(m+n)=f\left(m\right)+f\left(n\right)$ for every $m,n\in N.$ If $f\left(6\right)=18,$ then $f\left(2\right)\cdot f\left(3\right)$ is equal to

1. $54$
2. $18$
3. $6$
4. $36$

Q. Which of the following is a function in their respective given domain and co-domain?

1. $f:\{-1,0,1\}\to \{0,1,2,3\}f\left(x\right)=x^2+3$
2. $f:\{0,1,2\}\to \{-2,-1,0,1,2\}f\left(x\right)=\sqrt{x}$
3. $f:\{0,1,4\}\to \{-2,-1,0,1,2\}f\left(x\right)=-\sqrt{x}$
4. $f:\{-2,-1,0,1,2\}\to \{-1,0,1\}f\left(x\right)=-|x|$

Q.

Let $R=\left\{(a,a)\right\}$ be a relation on set $A$.Then $R$ is

1. Symmetric

2. Antisymmetric

3. Symmetric and antisymmetric

4. Neither symmetric nor antisymmetric

Q. If a function $f:\{1,2,3,4\}\to \{1,2,3,4,5,6,7,8,9\}$ is defined, then the function $f$ can be

1. $f\left(x\right)=2x+1$
2. $f\left(x\right)=|x|$
3. $f\left(x\right)=x^2$
4. $f\left(x\right)=x-1$

Q. What is the set of all first elements of the ordered pairs in a relation R from a set A to a set B called ?

Q. If $f:\{1,3,4\}\to C$, where $C$ is the co-domain of the function and $f\left(x\right)=x^2-3x+2$, then the co-domain of the function can be

1. Set of first $10$ whole numbers
2. Set of factors of $6$
3. Set of even integers
4. Set of natural numbers

Q. $X$ is a set of $3$ digit numbers divisible by $6$ and $Y$ is a set of $3$ digit numbers divisible by $4$, using the digits $0,1,2,3$ without repetition. The number of onto functions from $X$ to $Y$ is

1. $240$
2. $244$
3. $784$
4. $1024$

Q. Let R be the relation on Z defined by R ={(a, b):a, b $ϵ$ Z, a-b is an integer}.Find the domain and range of R

Q.

If $A$ is a set containing $10$ distinct elements, then the total number of distinct function from $A$ to $A$ is

1. ${10}^{10}$

2. $101$

3. $2^{10}$

4. $2^{10-1}$

Q. Let $f:R\to R$ be defined as $f\left(x\right)=\frac{x^2-x+4}{x^2+x+4}$. Then the range of the function $f\left(x\right)$ is

1. $[\frac{3}{5},\frac{5}{3}]$
2. $(\frac{3}{5},\frac{5}{3})$
3. $(-\infty ,\frac{3}{5})\cup (\frac{5}{3},\infty )$
4. $[-\frac{5}{3},-\frac{3}{5}]$

Q. If a function is defined from $A$ to $B$ as


then the total number of elements in co-domain of function is

Q. Which of the following is a function in their respective given domain and co-domain?

1. $f:\{-1,0,1\}\to \{0,1,2,3\}f\left(x\right)=x^2+3$
2. $f:\{0,1,2\}\to \{-2,-1,0,1,2\}f\left(x\right)=\sqrt{x}$
3. $f:\{0,1,4\}\to \{-2,-1,0,1,2\}f\left(x\right)=-\sqrt{x}$
4. $f:\{-2,-1,0,1,2\}\to \{-1,0,1\}f\left(x\right)=-|x|$

Q. Let $A=\{1,2,3\}$ and $B=\{1,4,7,12,15,18\}$. A function $f:A\to B$ is defined by $f\left(x\right)=x^2+3$. Then

1. range of $f$ is $\{4,7,12\}$
2. range of $f$ is $\{1,4,7,12\}$
3. co-domain of $f$ is $\{4,7,12\}$
4. co-domain of $f$ is $\{1,4,7,12,15,18\}$

Q. If a function is defined from $A$ to $B$ as


then the total number of elements in domain of function is

Q. If a function is defined from $A$ to $B$ as


then the total number of elements in co-domain of function is

Q. If $R$ is an anti symmetric relation in $A$ such that $(a,b),(b,a)\in R$ then

1. $a\ge b$
2. None of these
3. $a\le b$
4. $a=b$

Q. If a function is defined from $A$ to $B$ as


then the total number of elements in domain of function is

Q. Let $A=\{2,4,6,8\}$. A relation $R$ on $A$ is defined by $R=(2,4),(4,2),(4,6),(6,4)$. Then $R$ is:

1. $anti-symmetric$
2. $reflexive$
3. $symmetric$
4. $transitive$

Q. Suppose $f$ is a real-valued differentiable function defined on $[1,\infty )$ with $f\left(1\right)=1.$ Moreover, suppose that $f$ satisfies$f^{\prime }\left(x\right)=\frac{1}{x^2+f^2\left(x\right)}.$ Show that $f\left(x\right)<1+\frac{\pi }{4}\forall x\ge 1$

Q. If $f:\{1,3,4\}\to C$, where $C$ is the co-domain of the function and $f\left(x\right)=x^2-3x+2$, then the co-domain of the function can be

1. Set of first $10$ whole numbers
2. Set of factors of $6$
3. Set of even integers
4. Set of natural numbers

Q. Let R be a relation on Z (the set of integers) defined as $mRn$, $iffm\le n\forall m,n\in Z$ then R is anti symmetric.

Q. If $f:\{1,3,4\}\to C$, where $C$ is the co-domain of the function and $f\left(x\right)=x^2-3x+2$, then the co-domain of the function can be

1. Set of first $10$ whole numbers
2. Set of factors of $6$
3. Set of even integers
4. Set of natural numbers

Q. Which of the following relations are functions ? Give reasons. If it is a function determine its domain and range.
(i) $\left\{\right(2,1\left)\right(5,1),(8,1\left)\right(11,1\left)\right(14,1),(17,1\left)\right\}$

Q. Let $A=\{1,2,3\}$ and $B=\{1,4,7,12,15,18\}$. A function $f:A\to B$ is defined by $f\left(x\right)=x^2+3$. Then

1. range of $f$ is $\{4,7,12\}$
2. range of $f$ is $\{1,4,7,12\}$
3. co-domain of $f$ is $\{4,7,12\}$
4. co-domain of $f$ is $\{1,4,7,12,15,18\}$

Q. If a function $f:\{1,2,3,4\}\to \{1,2,3,4,5,6,7,8,9\}$ is defined, then the function $f$ can be

1. $f\left(x\right)=2x+1$
2. $f\left(x\right)=|x|$
3. $f\left(x\right)=x^2$
4. $f\left(x\right)=x-1$

Q. If a function defined from $A$ to $B$ as follows


Then the correct options is/are

1. Domain of function is $\{1,2,3,4,5\}$
2. Co-domain of function is $\{2,4,6,8,10\}$
3. Range of function is $\{2,4,6,8,10\}$
4. Co domain and range of the given function is same.