Answer the following questions
Question
- f= {(0, a), (1, d), (5, e), (11, f)} find the inverse of this function f-1?
- Insert keys 11, 26, 88, 55, 120, 44, 34, 135, 76, 81 into an array that has 16 slots by using Linear Probe method.
- f= {(1, a), (2, b), (3, a)} determine the type of this function?
- Determine whether each function is one to one, onto, or both. Prove your answer. The domain and codomain of each function is the set of all real numbers.
f(x)= 7x-10q
Next f(x)= 4x-3
f(x)= 2×3-4
Last f(x)= x/(1+x2) - Define a sequence S as sn= 3n+5*2n n³0
a) Find S0
b) Find S2
c) Find a formula for Si
d) Find a formula for Sn-1 - Determine the type of the sequences whether they are decreasing, increasing, non-decreasing, non-increasing? They can be more than one of the types.
a) The sequence ai= 2/i i³1
b) The sequence 200, 130, 130, 90, 90, 43, 43, 20
c) The sequence 50
Explanation
1.Answer
The given function f={ (a,0), (1,d), (5,e),(11,f) }
f={ (a,0), (d,1), (e,5), (f,11) }
2. Answer
Linear Probing:
→ 16 Slots (arr[16])
→ Inserting 11:
11 % 16=11 : arr[11]=11
→ 26 %18=10 : arr[10]=26
→ 88 % 16 =8 : arr[8]=88
→ 55 % 16 =7 : arr[7]=55
→ 120 % 16 =8 : collision at index 8 so, arr[9]=120
→ 44 % 16 =12 : arr[12]=44
→ 34 % 16 =2 : arr[2]=34
→ 76 % 16 =12 : Collision arr[14]=76
→ 81 % 16 =1 : arr[1]=81
| 81 | 34 | 55 | 88 | 180 | 86 | 11 | 44 | 155 | 76 | ||||||
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
3. Answer
f= { (1.a), (2,b), (3,a) }
range= codomain
Every element of the domain has a unique element in the domain
Therefore, Bijective function 4
4. Answer
- f(x)= 7x-10a (one to one)
- Next we have a, f(x)= 4x-3 (one to one)
- f(x)= 2x3-4 (one to one) (not onto)
- last, f(x)= x/1+x 2 (one to one)
5. Answer
So we have, Sn = 3n+5*2n+ 0*n3= 3n+5*2n
- S0= 30+5 *20 = 1+5=6
- S2 = 32+5*(22) = 29
- Si = 3I+5*(2i)
- Sn-1= 3n-1+5*2n-1
6. Answer
ai= 2/i + i 3 *1 = 2/i+i3
b. Sequence= 200,130,130,90,90,43,43,20
2/100 + (200)3
ai= i3
The sequence is non-increasing.
Also read, Z Three Numbers