Range, Domain and Codomain

Q. The relation R = {($x$, $x^2$) |$x$ is a prime number less than 13}. Find the range of R.

1. {2, 3, 5, 7}
2. {2, 3, 5, 7, 11}
3. {4, 9, 25, 49, 121}
4. {1, 4, 9, 25, 49, 121}

Q. Let f be a function from R to R defined by
f (x) = 3x − 5 . Find the values of a and b given that (a, 4) and (1, b) $\in$ f.

1. a = 3 and b = 2
2. a = 3 and b = -2
3. a = -3 and b = 2
4. a = -3 and b = -2

Q.

nP4=20(nP2) then find the value of n

Q.

Let $n(A-B)=25+x$, $n(B-A)=2x$ and $n(A\cap B)=2x$. If $n\left(A\right)=2\left(n\right(B\left)\right)$ then '$x$' is

1. 4

2. 5

3. 6

4. 7

Q. Let f be a function f : N $\to$ N defined by
f (x) = 3x +2, x $\in$ N. Find the pre-images of 29 and 53.

1. 9 and 17 respectively
2. 17 and 9 respectively
3. -9 and -17 respectively
4. -17 and -9 respectively

Q. Solve the matrix equation [41]*X=[(-4)8(-1)2]

Q. How to solve x3-6x2+11x-6 into (x-1)(x-2)(x-3)

Q. A Relation R is given by the set {(x, y) | y =
x + 3, x $\in$ {0, 1, 2, 3, 4, 5}}. Determine its domain and range.

1. Domain of R = {3, 4, 5, 6, 7, 8}
   ​​​​​​Range of R = {0, 1, 2, 3, 4, 5}
2. Domain of R = {0, 1, 2, 3, 4, 5}
   ​​​​​​Range of R = {3, 4, 5, 6, 7, 8}
3. Domain of R = {0, 1, 2, 3}
   ​​​​​​Range of R = {3, 4, 5, 6, }
4. Domain of R = {1, 2, 3, 4, 5}
   ​​​​​​Range of R = {4, 5, 6, 7, 8}

Q. Let f be a function f : N$\to$ N defined by f (x) = 3x + 2, x $\in$ N. Find the images of 1, 2, 3.

1. -5, 8, 11
2. 5, 8, 11
3. -5, -8, -11
4. 5, 8, -11

Q.

What is the image of $\left(-5,5\right)$ after a dilation by a scale factor of $4$ centered at the origin?

Q. Find the domain of real-valued function: $f\left(x\right)=\frac{2x+1}{x-9}$

1. R - {9}
2. R
3. R + {9}
4. R - {-9}

Q. If p(x) = – x 2 + px – p – 8 and p(x) < 0 for all real values of x, then the value of p cannot be

Q. If the function f(x) = 1 + kx , x is not equal to 0, is the inverse of itself, then the value of k is

Q. The expression $\frac{a^{n+1}+b^{n+1}}{a^n+b^n}is[a\ne b\ne 0]$ is (where a and b are unequal non-zero numbers)

1. G.M. between a and b$=-\frac{1}{2}$
2. A.M. between a and b if n = -1
3. all are correct
4. H.M. between a and b if n = 0

Q.

root 6 plus root 6 till infinity is equal to

Q.

The value/s of x when (x - 4) (3x + 2) = 0 ________

1. 4, -2/3

2. 4, 2/3

3. -4, - 2/ 3

4. -4, 2/3

Q. what is co domain , how to find co domain and how to find a relation R for a single set A for instance ?

Q.

1. (x – 2)(x – 1)(x – 4)

2. (x – 2)(x – 4)(x – 1)

3. (x – 1)(x – 2)(x – 5)

4. (x – 1)(x – 3)(x – 2)

Q. Find the domain of the function:
$f\left(x\right)=\frac{x^2+3x+5}{x^2-5x+4}$. [2 marks]

Q. what is Eulerian form of a complex number . explain.

Q. If $f\left(x\right)=\frac{4^x}{4^x+2}\mathrm{for}\mathrm{all}x\in R.$
Which of the following is/are true?

1. $f\left(x\right)=f(1-x)$
2. $f\left(x\right)+f(1-x)=0$
3. $f\left(x\right)+f(1-x)=1$
4. $f\left(x\right)+f(x-1)=1$

Q. A is the set of all the numbers on which a function is defined. It may be real as well.

1. domain
2. range
3. co-domain

Q. The product of all numbers is

1. -2
2. 1
3. 0
4. 2

Q.

The solution of (x +2 )² = 25 is

1. -3, -7

2. -3, 7

3. 3, -7

4. 3, 7

Q. The domain of the function $f\left(x\right)=\frac{1}{\sqrt{x-5}}$ is ___

1. $[5,\infty ]$
2. $(5,\infty ]$
3. R${}^{+}$
4. R

Q. For function f(x) = x + 2, image of 1 is ____

1. 1
2. 2
3. 3
4. Can't be found

Q. A relation xRy is from A to B, which of the following is always true about relation R?

1. Codomain = B
2. Range = B
3. n(A) = n(B)
4. Domain = A

Q. For function f(x) = 1/x, the value of domain can't be ____

1. 1
2. 2
3. 0
4. -1

Q. Show that there is no value of n for which (2ⁿ × 5ⁿ) ends in 5.

Q. For function f(x) = x + 2, image of 1 is ____