Absolute Values (1 Viewer)

[Web Addict]

Hi.

Just wondering, is abs(x-1) equal to abs(1-x)? There was a multiple-choice question in my Trial HSC for Mathematics Extension 2 and there were two options with something like this.

Thank you.

 

[Menomaths]

Hi.

Just wondering, is abs(x-1) equal to abs(1-x)? There was a multiple-choice question in my Trial HSC for Mathematics Extension 2 and there were two options with something like this.

Thank you.

Yeah it is, if you sub in random values it comes out same. But then you do 4 unit so now I'm unsure weather I'm correct or not.

 

[Web Addict]

The question asked us to integrate -secx using the substitution, t=tan(x/2). All of the options were in terms of t. (Sorry, but I don't know how to use the maths thing to make things look more mathematical and fancy.)

 

[HeroicPandas]

Yes because | - f | = f

OR using graphing techniques (if u have time)

draw y = x-1 and y = 1-x

then draw, y = |x-1| and y = |1-x|

u'll notice they are the same graph, so |x-1| = |1-x|

the graphing technique can be done mentally

 

[Menomaths]

I should be doing 4 unit :')

 

[RaceOfAce]

Just fiddle with it:

y = |1-x|
y = ±(1-x)

If you take out -1, the ± is the same (-1 * +1 = -1; -1 * -1 = +1):
y= ±(x-1)
y = |x-1|