Tuesday

July 22, 2014

July 22, 2014

Posted by **Jane** on Friday, November 23, 2007 at 3:32pm.

g(x)=2x+1

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.

Ans:

p(n):g^n

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.

**Related Questions**

Discrete Math - A factory makes automobile parts. Each part has a code ...

Discrete Math - A factory makes automobile parts, 5C7, 1O6 or 3Z0, which are of ...

Math Algebra - kassie an kesya are dividing $39 into two parts in order that the...

chemistry - The urine of horses are mixed with an excess of hydrochloric acid, ...

3rd grade - alice folded a piece of paper into 12 equal squares and colored them...

5th grade math (word problems) - I'm not sure how to solve the following problem...

Science - Why is it rare for the soft parts of an organism to become a fossil? A...

U.S.History - i have to analyze a political cartoon. it appeared during the ...

***Discrete Math *** - I'm not sure how to start part(a). I believe part (b) is ...

math - a bathroom cleaner contains 1 part of bleach with 4 parts of water. if ...