For each integer n, define fn: r-> r by fn(x)=x+n. a) prove that for each integer n, fn is a permutation of r, that is fnes( b)prove that fn•(• meaning composed)fm=fn+m and fn^-1=f-n c) let g={fn: nez}. prove that g is a subgroup of s(r). d) prove that g is cyclic (find a generator of g).

25

step-by-step explanation:

g = (2, 2)

step-by-step explanation:

given the ratio is 1 : 1 then f is the midpoint of eg

let the coordinates of g = (x, y)

using the midpoint formula

(0 + x) = 1 ( multiply both sides by 2 )

0 + x = 2 ⇒ x = 2

similarly

(4 + y) = 3 ( multiply both sides by 2 )

4 + y = 6 ( subtract 4 from both sides )

y = 2

coordinates of g = (2, 2)

cosine

step-by-step explanation:

6/20

step-by-step explanation: