Consider these functions: f(x)= -2x - 1
g(x)= -1/2x + 1/2
Which statements, if any, are true about these functions?
I. The function f(g(x)) = x for all real x.
II. The function g(f(x)) = x for all real x.
III. Functions f and g are inverse functions.

A. I only
B. II only
C. I, II, and III
D. None of the statements are true.

does anyone know how to do this

Part A)

Add up the probability values to get:

0.09+0.36+0.35+0.13+0.05+0.02 = 1

since we get 1 as a result, this confirms we have a legitimate probability distribution. 



Part B)

The notation P(X > 2) translates to "the probability that X is larger than 2". In this problem's context, it means "the probability of choosing a family that owns more than 2 cars"



Part C)

P(X = 2) means "the probability that X is equal to 2"

Specifically for this problem it means "the probability of picking a family with exactly 2 cars". 



Part D)

Let
A = probability that the family owns exactly 0 cars = 0.09
B = probability that the family owns exactly 1 cars = 0.36
C = probability that the family owns exactly 2 cars = 0.35
D = probability that the family owns exactly 3 cars = 0.13
E = probability that the family owns exactly 4 cars = 0.05
F = probability that the family owns exactly 5 cars = 0.02

Add up the probabilities D, E, and F to compute P(X > 2)

P(X > 2) = probability that the family owns more than 2 cars
P(X > 2) = D + E + F
P(X > 2) = 0.13+0.05+0.02
P(X > 2) = 0.2