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

1. Domain of a function is :

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

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

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

3. Range of a function is :

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

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

Explanation: Function x

^{-1}is not defined for x=0,otherwise it defined for every real number.

5. State whether the given statement is true or false

The range of function f(x) = sin(x) is (-∞, ∞).

a) True

b) False

View Answer

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

6. State whether the given statement is true or false

Codomain is the subset of range.

a) True

b) False

View Answer

Explanation: Range is the subset of codomain, that is every value in 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

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

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

9. If f(x) = x^{2} + 4 then range of f(x) is given by

a) [4, ∞)

b) (-∞, ∞) – {0}

c) (0, ∞)

d) None of the mentioned

View Answer

Explanation: Since minimum value of x

^{2}is 0,thus x

^{2}+4 may take any value between [4,∞).

10. State True or False.

Let f(x)=sin^{2}(x) + log(x) then domain of f(x) is (-∞, ∞).

a) True

b) False

View Answer

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

**Sanfoundry Global Education & Learning Series – Discrete Mathematics.**

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