f is strictly decreasing on R and f(a) > f(b). What can be said about a and b?

Increasing & Decreasing Functions · Question 6 of 74

Question 6

MediumOriginal question

$f$ is strictly decreasing on $\mathbb{R}$ and $f(a) > f(b)$ . What can be said about $a$ and $b$ ?

a > b

Correct answerYour answer

a = b

Correct answerYour answer

a < b

Correct answerYour answerNothing: either order is possibleCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

A strictly decreasing function reverses order: a smaller input gives a larger output.
If $a \ge b$ , then $f(a) \le f(b)$ , which is not what is given. So $a < b$ .

Worth noting

$a > b$ is the conclusion for an increasing function.

Ten questions from Increasing & Decreasing Functions, at your own pace.

Ten questions from Increasing & Decreasing Functions, at your own pace.