*** Discrete Math ***

posted by .

I have solved parts of the question, but I want to know if they are correct. Other parts I'm not sure how to do, like part b and c.

Define g^3= g^2 o g,...,g^n =g^(n-1) o g
(where "o" means composition)

a) Give rules for g^2, g^3, g^4

Ans: g^2= g o g= g(2x+1)= 4x+3
g^3= g^2 o g= g^2(2X+1)=8X+7
g^4= g^3 o g= g^3(2x+1)= 16x+15
b) Make a conjecture as to the general rule for g^n. for any positive integer n.
Ans: ? g^n= 2^(n-1) 2x+ 2^(n) -1

c) Verify conjecture by induction.

p(n)==> p(n+1)
Assume p(n),
prove g^(n+1)= 2^(n) 2x+ 2^(n+1)-1
*** (I'm not if the following is correct.)***

g^(n+1)=2^(n-1)2x+2^(n)-1 +(g^(n) o g)
If correct, how do I continue.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. 3rd grade

    alice folded a piece of paper into 12 equal squares and colored them. She had 3 times as many red parts as green parts and 2 more yellow parts than blue parts. How many parts did she have of eeach color?
  2. Math Algebra

    kassie an kesya are dividing $39 into two parts in order that the sum of 2/3 of one part and 3/4 of the other part is $28. What are the parts?
  3. Discrete Math

    A factory makes automobile parts. Each part has a code consisting of a letter and three digits, such as C117, O076, or Z920. Last week the factory made 60,000 parts. Prove that there are at least three parts that have the same serial …
  4. Discrete Math

    A factory makes automobile parts, 5C7, 1O6 or 3Z0, which are of 5,000 parts, what is the minimum number of parts with the same serial number?
  5. 5th grade math (word problems)

    I'm not sure how to solve the following problem: If you divide 1/10 of a dollar into parts that are each 1/100 of a dollar, how many parts are there?
  6. chemistry

    The urine of horses are mixed with an excess of hydrochloric acid, after some time, a yellowish-brown crystalline precipitate, which have an unpleasant odor, that can't be removed by simply washing with water. This new compound has …
  7. Statistics

    In a shipment of 21 parts, four of the parts are defective. If three parts are selected at random without replacement, find the probability that : a.) All three parts selected are defective. 4/21*3/20*2/19=.003 b.) None of the tree …
  8. Quantitative, stastics and business

    A company has three machines A, B and C which all produce the same two parts, X and Y. of all the parts produced, machine A produces 60%, machine B produces 30%, and machine C produces the rest. 40% of the parts made by machine A are …
  9. math

    a number is divided into two parts such that one part is 10 more than the other. if the two parts are in the ratio 5:3,find the number and the two parts?
  10. Math

    I need help not sure if I'm doing this correctly. Parts of parts: Find each of the following parts of parts without drawing a diagram for each problem explained clearly A) 2/3 of 2/7 I think it's 4/15 because your multiplying. B) 6/11 …

More Similar Questions