For each integer n, define f_n: r rightarrow r by f_n (x) = x + n. (a) prove that for each integer n, f_n is a permutation of r, that is f_n elementof s(r). (b) prove that f_n compositefunction f_m = f_n + m and f^-1_n = f_-n (c) let g = {f_n: n elementof z}. prove that g is a subgroup of s(r). (d) prove that g is cyclic (find a generator of g).

The system of equations graphed below has how many solutions?

Determine the difference: 3.2 × 1010 – 1.1 × 1010. write your answer in scientific notation.

According to the 2008 u. s. census, california had a population of approximately 4 × 10^7 people and florida had a population of approximately 2 × 10^7 people. which of the following is true? a. the population of florida was approximately two times the population of california. b. the population of florida was approximately twenty times the population of california. c. the population of california was approximately twenty times the population of florida. d. the population of california was approximately two times the population of florida.