Chapter 1.1, Problem 61E

Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.

1. a. The range of f(x) = 2x − 38 is all real numbers.
2. b. The relation y = x⁶ + 1 is not a function because y = 2 for both x = −1 and x = 1.
3. c. If f(x) = x⁻¹, then f(1/x) = 1/f(x).
4. d. In general, f(f(x)) = (f(x))².
5. e. In general, f(g(x)) = g(f(x)).
6. f. By definition, f(g(x)) = (f ∘ g)(x).
7. g. If f(x) is an even function, then c f(ax) is an even function, where a and c are nonzero real numbers.
8. h. If f(x) is an odd function, then f(x) + d is an odd function, where d is a nonzero real number.
9. i. If f is both even and odd, then f(x) = 0 for all x.