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

a. The range of f(x) = 2x - 38 is all real numbers.

b. The relation y = x⁶ + 1 is not a function because y = 2 for both x = -1 and x = 1.

c. If f(x) = x - 1, then f (1/x) = 1/f(x).

d. In general, f(f(x)) = (f(x))).

e. In general, f(g(x)) = g(f(x)).

f. By definition, f(g(x)) = (f ͦ g)(x).

g. If f(x) is an even function, then c f(ax) is an even function, where a and c are nonzero real numbers.

h. If f(x) is an odd function, then f(x) + d is an odd function, where d is a nonzero real number.

i. If f is both even and odd, then f(x) = 0 for all x.