DM Quiz Test

Which of the following is a function?

• f={(1,2),(1,3),(2,4)}

• f={(1,2),(2,3),(3,4)}

• f={(1,1),(2,2),(3,1),(2,3)}

• f={(2,3),(2,5),(3,6)}

The domain of the function f(x)=1/(x−4) is:

• x≠4

• x≠−4

• x=4

• All real numbers

The relation R={(a,b):a≤b} on the set of natural numbers is:

• Reflexive

• Symmetric

• Transitive

• None of the above

The number of relations that can be defined from set A={1,2,3} to B={4,5} is:

• 6

• 16

• 64

• 32

Which of the following functions is one-to-one (injective)?

• f(x)=x^2

• f(x)=x+2

• f(x)=|x|

• f(x)=x^3

The range of the function f(x)=x+5 is:

• [0,∞)

• (−∞,0]

• (5,∞)

• (−5,∞)

The inverse of the function f(x)=3x+7 is:

• f−1(x)=3(x−7)

• f−1(x)=3(x+7)

• f−1(x)=x/3−7

• f−1(x)=3x−7

If a function f:A→B is surjective (onto), which of the following is true?

• Every element of A is mapped to a unique element of B.

• Every element of B has a preimage in A.

• Every element of A has a preimage in B.

• f is one-to-one.

If the function f(x)=1/(x+1) is defined, what is the domain of f(x)?

• x≠−1

• x=1

• x≠1

• All real numbers

A relation R on set A={1,2,3} is called reflexive if:

• (a,a)∈R for all a∈A

• (a,b)∈R implies (b,a)∈R

• (a,b)∈R and (b,c)∈R imply (a,c)∈R

• None of the above