Mathematics Multiple Choice Questions on “Functions”.
1. In a function from set A to set B, every element of set A has___________ image in set B.
a) one and only one
b) different
c) same
d) many
Answer: a
Clarification: A relation from a set A to a set B is said to be a function if every element of set A has one and one image in set B.
2. In a function from set A to set B, image can have more than one preimage.
a) True
b) False
Answer: a
Clarification: A relation from a set A to a set B is said to be a function if every element of set A has one and one image in set B. A preimage must have one image, an image can have more than one preimage.
3. Let R be a relation defined on set of natural numbers {(x, y): y=2x}. Is this relation can be called a function?
a) True
b) False
Answer: a
Clarification: Since every natural number has one and only image so this relation can be called a function.
4. Which of the following is not a function?
a) {(1,2), (2,4), (3,6)}
b) {(-1,1), (-2,4), (2,4)}
c) {(1,2), (1,4), (2,5), (3,8)}
d) {(1,1), (2,2), (3,3)}
Answer: c
Clarification: A relation from a set A to a set B is said to be a function if every element of set A has one and one image in set B.
In {(1,2), (1,4), (2,5), (3,8)}, since element 1 has two images 2 and 4 which is not possible in a function so, it is not a function. Rest all have one and only one image so they can be called a function.
5. f(x) = {(frac{|x|}{x}) for x≠0 and 0 for x=0}. Which function is this?
a) Constant
b) Modulus
c) Identity
d) Signum function
Answer: d
Clarification: f(x) = {(frac{|x|}{x}) for x≠0 and 0 for x=0}. Function is {(-3, -1), (-2, -1), (-1,1), (0,0), (1,1), (2,1), (3,1), …….}. This is signum function.
6. Find domain of function |x|.
a) Set of real numbers
b) Set of positive real numbers
c) Set of integers
d) Set of natural numbers
Answer: a
7. Find range of function |x|.
a) Set of real numbers
b) Set of positive real numbers
c) Set of integers
d) Set of natural numbers
Answer: b
8. f(x) = (sqrt{9-x^2}). Find the domain of the function.
a) (0,3)
b) [0,3]
c) [-3,3]
d) (-3,3)
Answer: c
Clarification: We know radical cannot be negative. So, 9-x,2 ≥ 0
(3-x) (3+x) ≥ 0 => (x-3) (x+3) ≤ 0 => x∈[-3,3].
9. f(x) = (sqrt{9-x^2}). Find the range of the function.
a) R
b) R+
c) [-3,3]
d) [0,3]
Answer: d
Clarification: We know, square root is always non-negative. So, (sqrt{9-x^2}) ≥ 0. So, range of the function is set of positive real numbers.