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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.

Verified Answer :

konrad509

\(p \ \textless \ q, f(p) \ \textless \ f(q)\) 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:

option B is correct.

Step-by-step 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.



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