Question

Define "f: R → R" by the rule "f(x) = -x" for all real numbers. What is "(f ◦ f)(x)"?

a. "(f ◦ f)(x) = -x"
b. "(f ◦ f)(x) = x"
c. "(f ◦ f)(x) = -(-x)"
d. "(f ◦ f)(x) = -(x)"

Answer 1

The composition of the given function f(x) = -x is equal to x.

Step-by-step explanation:

The given function is defined as f(x) = -x for all real numbers. The composition of two functions is denoted as (f ◦ f)(x), which means applying f twice to the input x. To find (f ◦ f)(x), we substitute f(x) into itself: (f ◦ f)(x) = f(f(x)).

Plugging in f(x) = -x, we have (f ◦ f)(x) = -(-x) = x. Therefore, the correct answer is c. '(f ◦ f)(x) = -(-x)'.