1. If rxty = +1 and rx2y = -1, can you tell what happens to rxy when we combine x1 and x2 into a new variable? Make and provide your own data for your demonstration.

In Problems 39–46, show that (f ° g) (x) = (g° f) (x) = x. %3D 39. f(x) = 2x; g(x) = 40. f(x) = 4x; g(x) = i* 41. f(x) = x; g(x) %3! %3D 43. f(x) = 2x – 6; 8(x) = ; (x + 6) 46. fl+) = s(*) = 42. f(x) = x + 5; g(x) = x - 5 44. f(x) = 4 – 3x; g(x) = (4 - x) %3D 45. f(x) = ax + b; g(x) = - (x - b) a + 0 %3D a

Hermann Ebbinghaus (1850–1909) pioneered the study of memory. A 2011 article in the Journal of Mathematical Psychology presents the mathematical model R(t) = a + b(1 + ct)−? for the Ebbinghaus forgetting curve, where R(t) is the fraction of memory retained t days after learning a task; a, b, and c are experimentally determined constants between 0 and 1; ? is a positive constant; and R(0) = 1. The constants depend on the type of task being learned. (a) What is the rate of change of retention t days after a task is learned?