1. Which of the following is(are) true for the given function?

f:R→R

f(x)=x² +2

𝑅 is a set of real numbers.

• • • • 𝑓 is not injective

      • 𝑓 is bijective

      • 𝑓 is surjective

      • 𝑓 is not surjective

Correct Answer : 𝑓 is not injective, 𝑓 is not surjective

2. Consider the following table:

We can think of this as a function 𝑓 from the set of students to the set of integers between 160 and 170. Now pick out the correct statement from the following.

• 𝑓 is onto but not one-to-one.

• 𝑓 is bijective.

• 𝑓 is one to one but not onto.

• 𝑓 is neither one to one nor onto.

Correct Answer : 𝑓 is neither one to one nor onto.

3. Let 𝑓:𝑅→𝑅 such that f(x)= x/2 +7

• 𝑓 is not a function

• 𝑓 is bijective

• 𝑓 is injective

• 𝑓 is surjective

Correct Answer : 𝑓 is bijective

4. If a function is defined as f(x)=2x+15 then the value of f^-1 (25) is

• 3

• 5

• 39

• 25

Correct Answer : 5

5. Set 𝐶 has cardinality 𝑝 and a total of 5040 bijective functions. What is the value of 𝑝² ?

• 144

• 25

• 81

• 49

Correct Answer : 49

6. find the domain and range of the following real-valued function. f(x)= √3 -x

• domain={𝑥 ∈ R | 𝑥 ≤ 3}

range={𝑥 ∈ R | 𝑥 ≤ 0}

• domain={𝑥 ∈ R | 𝑥 ≠ 3}

range={𝑥 ∈ R|𝑥 ≥ 3}

• domain={𝑥 ∈ R | 𝑥 ≥ 3}

range={𝑥 ∈ R | 𝑥 ≥ 0}

• domain={𝑥 ∈ R | 𝑥 ≤ 3}

range={𝑥 ∈ R | 𝑥 ≥ 0}

Correct Answer : domain={𝑥 ∈ R | 𝑥 ≤ 3}

range={𝑥 ∈ R | 𝑥 ≥ 0}

7. If 𝑓 and 𝑔 are function from 𝑅 to 𝑅 and f(x)=3x² + x − 13 and g(x)= 20/3x+8 then

fog(12)

• −267 / 49

• 20 / 1301

• −1443 / 121

• 5 / 11

Correct Answer :−1443 / 121

8. Let us define a function 𝑓:Z→Z as follows, f(x)={ x/ 2 if x is even; 0 if x is odd Z is a set of integers.

• onto but not one-to-one.

• one-to-one but not onto.

• one-to-one and onto.

• neither one-to-one nor onto.

Correct Answer : onto but not one-to-one.

9. The relation 𝑅 is defined as 𝑅 = {(𝑥,y) : 𝑥 ,y ∈ N, 𝑥 + y = 5} then the range is?

• {2,4}

• {2,3,4}

• {2,3}

• 4 and 9

Correct Answer : 4 and 9

10. Let 𝐴 be set with cardinality 𝑛 and set 𝐵 with cardinality 𝑚, there are a total of 3024 one to one functions from 𝐴 to 𝐵, what are the values of 𝑛 and 𝑚 respectively?

• 4 and 8

• 4 and 9

• 6 and 7

• 7 and 6

Correct Answer : 4 and 9

WEEK-5 DETAILED SOLUTION