Functions Domain and Range - Discrete Mathematics Multiple Choice Questions

This set of Discrete Mathematics MCQs focuses on “Domain and Range of Functions”.

1. What is the domain of a function?
a) the maximal set of numbers for which a function is defined
b) the maximal set of numbers which a function can take values
c) it is a set of natural numbers for which a function is defined
d) none of the mentioned
View Answer

Answer: a
Explanation: Domain is the set of all the numbers on which a function is defined. It may be real as well.

2. What is domain of function f(x)= x^1/2?
a) (2, ∞)
b) (-∞, 1)
c) [0, ∞)
d) None of the mentioned
View Answer

Answer: c
Explanation: A square root function is not defined for negative real numbers.

3. What is the range of a function?
a) the maximal set of numbers for which a function is defined
b) the maximal set of numbers which a function can take values
c) it is set of natural numbers for which a function is defined
d) none of the mentioned
View Answer

Answer: b
Explanation: Range is the set of all values which a function may take.

4. What is domain of function f(x) = x^-1 for it to be defined everywhere on domain?
a) (2, ∞)
b) (-∞, ∞) – {0}
c) [0, ∞)
d) None of the mentioned
View Answer

Answer: b
Explanation: Function x^-1 is not defined for x=0, otherwise it defined for every real number.

5. The range of function f(x) = sin(x) is (-∞, ∞).
a) True
b) False
View Answer

Answer: b
Explanation: A sine function takes values between -1 and 1,thus range is [-1, 1].

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6. Codomain is the subset of range.
a) True
b) False
View Answer

Answer: b
Explanation: Range is the subset of codomain, that is every value in the range is in codomain but vice-versa it is not true.

7. What is range of function f(x) = x^-1 which is defined everywhere on its domain?
a) (-∞, ∞)
b) (-∞, ∞) – {0}
c) [0, ∞)
d) None of the mentioned
View Answer

Answer: a
Explanation: Function x^-1 may take any real number hence it’s range is all real numbers.

8. If f(x) = 2^x then range of the function is?
a) (-∞, ∞)
b) (-∞, ∞) – {0}
c) (0, ∞)
d) None of the mentioned
View Answer

Answer: c
Explanation: The function cannot take negative values,hence range is (0, ∞).

9. If f(x) = x² + 4 then range of f(x) is given by?
a) [4, ∞)
b) (-∞, ∞) – {0}
c) (0, ∞)
d) None of the mentioned
View Answer

Answer: a
Explanation: Since minimum value of x² is 0, thus x² +4 may take any value between [4,∞).

10. Let f(x)=sin²(x) + log(x) then domain of f(x) is (-∞, ∞).
a) True
b) False
View Answer

Answer: b
Explanation: Domain is (0, ∞), since log(x) is not defined for negative numbers and zero.

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