Increasing/decreasing functions can't be even, but can be odd, so it's B.
f(x) can be odd or even.
let's take two functions y(x) = sin(x) odd. and y(x) =
both functions are odd and even respectivaly both meet the constraints established in the problem.
by graphing and visully inspecting it can be verified.
option B is correct.
we are given that for any p<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.
The answer is B) f(x) can be odd but cannot be even