This set of Discrete Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Functions”.

1. A function is said to be ______________, if and only if f(a) = f(b) implies that a = b for all a and b in the domain of f.

a) One-to-many

b) One-to-one

c) Many-to-many

d) Many-to-one

View Answer

Explanation: A function is one-to-one if and only if f(a)≠f(b) whenever a≠b.

2. The function f(x)=x+1 from the set of integers to itself is onto. Is it True or False?

a) True

b) False

View Answer

Explanation: For every integer “y” there is an integer “x ” such that f(x) = y.

3. The value of ⌊1/2.⌊5/2⌋ ⌋ is _______________.

a) 1

b) 2

c) 3

d) 0.5

View Answer

Explanation: The value of ⌊5/2⌋ is 2 so, the value of ⌊1/2.2⌋ is 1.

a) f(a, b) = a + b

b) f(a, b) = a

c) f(a, b) = |b|

d) f(a, b) = a – b

View Answer

Explanation: The function is not onto as f(a)≠b.

5. The domain of the function that assign to each pair of integers the maximum of these two integers is ________.

a) N

b) Z

c) Z ^{+ }

d) Z^{+ } X Z^{+ }

View Answer

Explanation: The domain of the integers is Z

^{+ }X Z

^{+ }.

6. Let f and g be the function from the set of integers to itself, defined by f(x) = 2x + 1 and g(x) = 3x + 4. Then the composition of f and g is ________.

a) 6x + 9

b) 6x + 7

c) 6x + 6

d) 6x + 8

View Answer

Explanation: The composition of f and g is given by f(g(x)) which is equal to 2(3x + 4) + 1.

7. __________ bytes are required to encode 2000 bits of data,

a) 1

b) 2

c) 3

d) 8

View Answer

Explanation: Two bytes are required to encode 2000 (actually with 2 bytes you can encode up to and including 65,535.

^{3}+ 2 is __________.

a) f

^{ -1 }(y) = (y – 2)

^{ 1/2 }

b) f

^{ -1 }(y) = (y – 2)

^{ 1/3 }

c) f

^{ -1 }(y) = (y)

^{ 1/3 }

d) f

^{ -1 }(y) = (y – 2)

View Answer

Explanation: To find the inverse of the function equate f(x) then find the value of x in terms of y such that f

^{ -1 }(y) = x.

9. The function f(x) = x^{3} is bijection from R to R. Is it True or False?

a) True

b) False

View Answer

Explanation: The function f(x) = x

^{3}is one to one as no two values in domain are assigned the same value of the function and it is onto as all R of the co domain is images of elements in domain.

10. The g ^{-1}({0}) for the function g(x)= ⌊x⌋ is ________.

a) {x | 0 ≤ x < 1}
b) {x | 0 < x ≤ 1}
c) {x | 0 < x < 1}
d) {x | 0 ≤ x ≤ 1}
[expand title="View Answer"] Answer: d
Explanation: g({0}) for the function g(x) is {x | 0 ≤ x ≤ 1}. Put g(x) = y and find the value of x in terms of y such that ⌊x⌋ = y.
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**Sanfoundry Global Education & Learning Series – Discrete Mathematics.**

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