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

The given function f={ (a,0), (1,d), (5,e),(11,f) }
f={ (a,0), (d,1), (e,5), (f,11) }

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

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

So we have, S_n = 3ⁿ+5*2ⁿ+ 0*n³= 3ⁿ+5*2ⁿ

a_i= 2/i + i ³ *1 = 2/i+i³

b. Sequence= 200,130,130,90,90,43,43,20

2/100 + (200)³

a_i= i³

The sequence is non-increasing.