Determine whether the following statements are true and give an explanation or counterexample.

a. A function could have the property that f(-x) = f(x), for all x.

b. cos (a + b) = cos a + cos b, for all a and b in [0, 2π].

c. If f is a linear function of the form f(x) = mx + b, then f(u + v) = f(u) + f(v), for all u and v.

d. The function f(x) = 1 - x has the property that f(f(x)) = x.

e. The set {x: |x + 3| > 4} can be drawn on the number line without lifting your pencil.

f. log₁₀(xy) = (log₁₀ x)(log₁₀ y)

g. sin^-1 (sin (2π)) = 0