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# Discrete Mathematics | Week 5

## Quiz

1. Which of the following is(are) true for the given function?
f: R → R
f(x)=x2+
2 where, R is a set of real number

a. 𝑓 is not injective

d.  𝑓 is not surjective

Explanation

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.

d. 𝑓 is neither one to one nor onto

Explanation

3. Let 𝑓: 𝑅→𝑅 such that f(x)=x/2+7

b. 𝑓 is bijective

Explanation

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

b. 5

Explanation

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

d. 49

Explanation

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

d. domain= {𝑥 ∈ R | 𝑥 ≤ 3}
range=
{𝑥 ∈ R | 𝑥 ≥ 0}

Explanation

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) is.

c. −1443/121

Explanation

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.

a. onto but not one-to-one

Explanation

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

d. {1,2,3,4}

Explanation

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

b. 4 and 9

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