Discrete Mathematics

Functions

Question 1
Marks : +2 | -2
Pass Ratio : 100%
The g -1({0}) for the function g(x)= ⌊x⌋ is ___________
{x | 0 ≤ x < 1}
{x | 0 < x ≤ 1}
{x | 0 < x < 1}
{x | 0 ≤ x ≤ 1}
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.
Question 2
Marks : +2 | -2
Pass Ratio : 100%
The value of ⌊1/2.⌊5/2⌋ ⌋ is ______________
1
2
3
0.5
Explanation:
The value of ⌊5/2⌋ is 2 so, the value of ⌊1/2.2⌋ is 1.
Question 3
Marks : +2 | -2
Pass Ratio : 100%
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 ____________
6x + 9
6x + 7
6x + 6
6x + 8
Explanation:
The composition of f and g is given by f(g(x)) which is equal to 2(3x + 4) + 1.
Question 4
Marks : +2 | -2
Pass Ratio : 100%
Which of the following function f: Z X Z → Z is not onto?
f(a, b) = a + b
f(a, b) = a
f(a, b) = |b|
f(a, b) = a – b
Explanation:
The function is not onto as f(a)≠b.
Question 5
Marks : +2 | -2
Pass Ratio : 100%
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.
One-to-many
One-to-one
Many-to-many
Many-to-one
Explanation:
A function is one-to-one if and only if f(a)≠f(b) whenever a≠b.
Question 6
Marks : +2 | -2
Pass Ratio : 100%
The inverse of function f(x) = x3 + 2 is ____________
f -1 (y) = (y – 2) 1/2
f -1 (y) = (y – 2) 1/3
f -1 (y) = (y) 1/3
f -1 (y) = (y – 2)
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.
Question 7
Marks : +2 | -2
Pass Ratio : 100%
__________ bytes are required to encode 2000 bits of data.
1
2
3
8
Explanation:
Two bytes are required to encode 2000 (actually with 2 bytes you can encode up to and including 65,535.
Question 8
Marks : +2 | -2
Pass Ratio : 100%
The function f(x)=x+1 from the set of integers to itself is onto. Is it True or False?
True
False
Explanation:
For every integer “y” there is an integer “x ” such that f(x) = y.
Question 9
Marks : +2 | -2
Pass Ratio : 100%
The function f(x) = x3 is bijection from R to R. Is it True or False?
True
False
Explanation:
The function f(x) = x3 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 the domain.
Question 10
Marks : +2 | -2
Pass Ratio : 100%
The domain of the function that assign to each pair of integers the maximum of these two integers is ___________
N
Z
Z +
Z+ X Z+
Explanation:
The domain of the integers is Z+ X Z+.