Read the two statements and choose the correct option. I. If f and g are strictly increasing on R, then f + g is strictly increasing on R. II. If f and g are strictly increasing on R, then fg is strictly increasing on R.

Increasing & Decreasing Functions · Question 28 of 74

Question 28

HardOriginal question

Read the two statements and choose the correct option.
I. If $f$ and $g$ are strictly increasing on $\mathbb{R}$ , then $f + g$ is strictly increasing on $\mathbb{R}$ .
II. If $f$ and $g$ are strictly increasing on $\mathbb{R}$ , then $fg$ is strictly increasing on $\mathbb{R}$ .

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

For $x_1 < x_2$ , $f(x_1) < f(x_2)$ and $g(x_1) < g(x_2)$ ; adding gives I.
$f(x) = g(x) = x$ are increasing, but $fg = x^2$ falls on $(-\infty, 0)$ , so II is false.

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

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