Read the two statements and choose the correct option. I. f(x) = 1/x is strictly decreasing on (0, ∞). II. f(x) = 1/x is strictly decreasing on its whole domain, all x ≠ 0.

Question 11

MediumOriginal question

Read the two statements and choose the correct option.
I. $f(x) = \frac{1}{x}$ is strictly decreasing on $(0, \infty)$ .
II. $f(x) = \frac{1}{x}$ is strictly decreasing on its whole domain, all $x \ne 0$ .

Only ICorrect answerYour answerOnly IICorrect answerYour answerBoth I and IICorrect answerYour answerNeither I nor IICorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

I: for $0 < x_1 < x_2$ , $\frac{1}{x_1} > \frac{1}{x_2}$ . True.
II: $-1 < 1$ but $f(-1) = -1 < f(1) = 1$ , so across the gap at 0 the function does not fall. False.

Worth noting

$f'(x) = -\frac{1}{x^2} < 0$ on each side of 0, but the derivative test works on one interval at a time.

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