In Exercises 9–16, determine whether the function is even, odd, or neither.

𝔂 = x⁴ + 1

x³ - 2x

In Exercises 9–16, determine whether the function is even, odd, or neither.

𝔂 = x - sin x

In Exercises 9–16, determine whether the function is even, odd, or neither.

𝔂 = x cos x

Suppose that ƒ and g are both odd functions defined on the entire real line. Which of the following (where defined) are even? odd?

a. ƒg

b. ƒ³

c. ƒ(sin x)

d. g(sec x)

e. |g|

In Exercises 5–8, determine whether the graph of the function is symmetric about the 𝔂-axis, the origin, or neither.

𝔂 = x² - 2x - 1

In Exercises 9–16, determine whether the function is even, odd, or neither.

𝔂 = 1 - cos x

In Exercises 9–16, determine whether the function is even, odd, or neither.

𝔂 = x² + 1