Question

how do I find G(x)= 3x + IxI over x ?

Answer 1

\[G(x)=\frac{x+|x|}{x}\] depends on whether x is positive or negative.
if x is negative then it is 0

Answer 2

if x is positive it is 2
and if x is zero it is undefined

Answer 3

ok you had
\[G(x)=\frac{3x+|x|}{x}\] make the necessary changes and you will have it

Answer 4

how did u get two for the answer or is that a rule ?

Answer 5

what is always true is that
\[|x|= x \text{ if } x\geq 0\] and

\[|x|=-x \text{ if } x < 0\] so you have to break it up into two cases
i guess you could say it is a rule; it is the definition of absolute value

Answer 6

easy with an example. suppose x was -2
then |x|=2 and you would have
\[\frac{3\times -2+2}{-2}=\frac{-6-2}{-2}=\frac{-8}{-2}=2\] any other negative number will give you two as well. try it

Answer 7

aah yes, can u explain why my book answer is \[(-\infty,0) \cup (0,\infty)\]