Determine whether each of the following functions is even, odd, or neither even nor odd.(a)  f(x) = x7 + x        (b)  g(x) = 1 − x2        (c)  h(x) = 2x − x4

Sure, let's determine whether each function is even, odd, or neither.

(a) f(x) = x^7 + x

A function is even if f(x) = f(-x) and odd if f(-x) = -f(x). Let's check:

f(-x) = (-x)^7 + (-x) = -x^7 - x which is not equal to f(x) = x^7 + x, so it's not even.

Also, -f(x) = -(x^7 + x) = -x^7 - x which is equal to f(-x), so it's odd.

(b) g(x) = 1 - x^2

g(-x) = 1 - (-x)^2 = 1 - x^2 which is equal to g(x), so it's even.

Also, -g(x) = -(1 - x^2) = x^2 - 1 which is not equal to g(-x), so it's not odd.

(c) h(x) = 2x - x^4

h(-x) = 2(-x) - (-x)^4 = -2x - x^4 which is not equal to h(x), so it's not even.

Also, -h(x) = -(2x - x^4) = -2x + x^4 which is not equal to h(-x), so it's not odd.

So, f(x) is odd, g(x) is even, and h(x) is neither even nor odd.