Suppose f(x) is a function such that if p

f(x) can be odd or even.

Step-by-step explanation:

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.

Step-by-step explanation:

we are given that for any p

f(p)

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