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Algebra Level 2

Which of the following equations about absolute value function is/are true for real values of x x ?

A. ∣ x ∣ = { x , x ≥ 0 − x , x < 0 |x| =\begin{cases} x &, x \geq 0 \\ -x & , x<0 \end{cases} .

B. ∣ x ∣ = max ⁡ { x , − x } |x|=\max \{ x, -x \} .

Neither A nor B Both A and B B A

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Sandeep Bhardwaj by Sandeep Bhardwaj , 28, India

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1 solution

Shanthanu Rai
Feb 17, 2016

A. is the definition of absolute value function. So, it is true. B. is also true as x is greater than -x for all positive real no.s including 0 (where x and -x are both equal). -x is greater than x for all negative real no.s.
So B. is same as A.

3 Helpful 0 Interesting 0 Brilliant 0 Confused

How about complex values of x...?

Manuel Kahayon - 5 years, 3 months ago

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Thanks. I have edited the problem for clarity.

Calvin Lin Staff - 5 years, 3 months ago

I REALLY disagree with the answer to this. The function reaches a turning point at 0. The function is neither increasing or decreasing at 0. If anything it is mirroring the line x=0.

Riho Sikes - 5 years, 3 months ago

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What are you disagreeing about? Your comment about turning point, increasing, decreasing have nothing to do with the stated question.

Calvin Lin Staff - 5 years, 3 months ago

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