Show that increasing functions and decreasing functions are one-to-one. That is, show that for any x₁ and x₂ in I, x₂ ≠ x₁ implies f(x₂) ≠ f(x₁).

Find the largest interval on which the given function is increasing.

c. g(x) = (3x - 1)¹/³

Is x¹² an even or odd function? Is sin x² an even or odd function?

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

a. The variable y = t + 1 doubles in value whenever t increases by 1 unit.

Which of the functions graphed in Exercises 1–6 are one-to-one, and which are not?

17. Even-odd decompositions

b. If f(x) = f_E(x) + f_O(x) is the sum of an even function f_E(x) and an odd function f_O(x), then show that

f_E(x) = (f(x)+f(-x))/2 and f_O(x) = (f(x)-f(-x))/2

In Exercises 7–10, determine from its graph if the function is one-to-one.

f(x) = 3 - x, x < 0

= 3, x ≥ 0

In Exercises 7–10, determine from its graph if the function is one-to-one.

f(x) = 1 - x/2, x ≤ 0

x/(x + 2), x > 0

State whether the functions represented by graphs A , B , C and in the figure are even, odd, or neither. <IMAGE>