Which of the following is always true of odd functions?f (-x) = -f(x)f(|x|) is even|f(x)| is even

The statement that is always true for odd functions is f(-x) = -f(x). This is the definition of an odd function: a function is odd if and only if it is symmetric with respect to the origin. This means that if you take the negative of the input (x), it is equivalent to taking the negative of the output (f(x)).

The other two statements are not necessarily true for odd functions:

• f(|x|) is even: This is not always true for odd functions. The absolute value function |x| is even, but applying an odd function to it does not necessarily result in an even function.

• |f(x)| is even: This is also not always true for odd functions. Taking the absolute value of an odd function does not necessarily result in an even function.