f is strictly increasing on R. Which describes g(x) = f(-x)?

Increasing on one part of R and decreasing on another

Question 7

MediumOriginal question

$f$ is strictly increasing on $\mathbb{R}$ . Which describes $g(x) = f(-x)$ ?

Strictly increasing on

\mathbb{R}

Correct answerYour answerStrictly decreasing on

\mathbb{R}

Correct answerYour answerIncreasing on one part of

\mathbb{R}

and decreasing on anotherCorrect answerYour answerIt depends on

f

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

For $x_1 < x_2$ , $-x_1 > -x_2$ , and $f$ keeps order, so $f(-x_1) > f(-x_2)$ .
That is $g(x_1) > g(x_2)$ : $g$ is strictly decreasing on $\mathbb{R}$ , whatever $f$ is.

Worth noting

Replacing $x$ by $-x$ reflects the graph in the $y$ -axis, which turns rising into falling.

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