Question

Suppose f(x) is a function such that if p < q, f(p) < f(q). Which statement best describes f(x)?

A.) -f(x) can be odd or even.
B.) -f(x) can be odd but cannot be even.
C.) -f(x) can be even but cannot be odd.
D.) -f(x) cannot be odd or even.

Answer 1

`p \ \textless \ q, f(p) \ \textless \ f(q)` means that the function
`f(x)` is increasing.
`-f(x)` is therefore decreasing.

Increasing/decreasing functions can't be even, but can be odd, so it's B.

Answer 2

option B is correct.

Explanation:

we are given that for any p<q

f(p)<f(q)

this clearly implies that f is an increasing function.

Now we know that if f is an increasing function then -f is always an decreasing function and vice-versa.

so here -f(x) will be an decreasing function.

Let us consider a example f(x)=x then f(x) is clearly an increasing function.

and -f(x)= -x is an decreasing function. also it is an odd function but not an even function.

so option B holds.