Final answer:
The expression f(-x) reflects the value of function f for the negation of x. Whether f(-x) equals -f(x) or f(x) depends on whether f is an odd or even function. Options c and d represent specific functions, not general relationships.
Step-by-step explanation:
The function f(-x) represents the value of the function f when its input is the negation of x. This expression does not inherently define the relationship between f(-x) and f(x) without additional information about the function's properties, such as whether it's an odd or even function. To determine if one of the options a. f(-x) = -f(x), b. f(-x) = f(x), c. f(-x) = -x, or d. f(-x) = x correctly represents f(-x) for a given function, we must know the specific form or properties of that function.
For example, for an even function (symmetric about the y-axis), option b would be correct: f(-x) = f(x). For an odd function (symmetric with respect to the origin), option a would be correct: f(-x) = -f(x). Options c and d describe specific types of functions rather than the general relationship between f(-x) and f(x).