Question

assume that f(1) =0 and that for all integers m and n f( m n) = f(m) f(n) 3(4mn-1) then f(19) is

Answer 1

f(m+n) = f(m)+f(n) + 3(4mn-1)
f(2) = f(1+1) = f(1)+f(1) + 3(3) = 9

f(4) = f(2+2) = f(2)+f(2)+ 3(15) = 18+45 = 63

f(8) = 126+3(63)= 315

f(16) = 630 + 765 = 1395

f(18) = f(16+2) = 1395+ 9 + 3(127) = 1785

f(19) = f(18+1) = 1785+0 + 213 =  1998

Answer 2

Answer:

Concept:

Latin was used to adapt the word "integer" for use in mathematics. The integer is defined as complete or whole. Although integers are quite similar to whole numbers, they also contain negative numbers.

Step-by-step explanation:

An integer is any positive or negative number, including zero, that has no decimal or fractional parts. Integer examples include: -5, 0, 1, 5, 8, 97, and 3,043. Z is a set of integers that consists of the following:

Positive Integers: If an integer is bigger than zero, it is considered positive. For instance, 1, 2, 3, etc.

When an integer is less than zero, it is said to be negative. For instance: -1,- 2,- 3, etc.

Zero is described as an integer that is neither negative nor positive. A whole number, that is.

Given:

Given f(m+n)=f(n)+3(4mn−1), f(1)=0

Find:

f(19)

Solution:

 Given f(m+n)=f(n)+3(4mn−1),f(1)=0

 Put n=1   ⟹f(m+1)=f(1)+3(4m−1)

                            =12m−3

Let m=18

   ⟹  f(18+1)=12×18−3

                    =216−3

                    =213

            f(19) = 213

         

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