Question

Give the definition of the modulus function R -> R, often denoted by x -> |x|. (This is also
called the absolute value function.)

Draw the graph of the function R -> R defined by x -> ||x - 1| -2|.
Express {x e R ||x-2| < 3g as} an open interval (a; b) for suitable a; b e R.

Answer 1

try this graph
http://www.wolframalpha.com/input/?i= ||x-1|-2|

Answer 2

First question : (PNG image)
http://tinyurl.com/3sql2qk

Answer 3

Or more correctly according to the question : http://tinyurl.com/3g98cew

Answer 4

cheers guys, any ideas how to do the last part?

Answer 5

is the graph clear? because i can send it step by step

Answer 6

\[|x-1|\]

Answer 7

\[|x-1|-2\]

Answer 8

thanks for that, i get it.

Answer 9

any ideas for last part?

Answer 10

\[||x-1|-2|\]

Answer 11

i don't really understand what the last one says. are you supposed to write this as a piecewise function?

Answer 12

it says "express
\[|x-2|<3g\] as an open interval?

Answer 13

i am confused by the question. if that is what it is asking, then i think the answer is easy.
if g = 0 you get x = 2
if g < 0 no answer
if g > 0 you solve
\[|x-2|<3g\]
\[-3g<x-2<3g\]
\[2-3g<x<2+3g\] so open interval is \[(2-3g,2+3g)\]

Answer 14

yes, sorry

Answer 15

ok then that is the answer above.

Answer 16

thanks very much, i get it now. appreciate it

Answer 17

yw