range

• Mar 28th 2011, 08:57 AM
prasum
range
find the range of mod(x-1)/x-1
• Mar 28th 2011, 10:01 AM
FernandoRevilla
Quote:

Originally Posted by prasum
find the range of mod(x-1)/x-1

Make a sketch of $f(x)=(x-1)/(x+1)=1-(2/(x+1))$ and by symmetry, of $|f(x)|$ . You'll easily find $\textrm {rg} (|f|)=[0,+\infty)$ .
• Mar 29th 2011, 01:50 AM
prasum
it is x-1 not x+1
• Mar 29th 2011, 02:00 AM
FernandoRevilla
Quote:

Originally Posted by prasum
it is x-1 not x+1

Sorry, my bad. What have you tried so far?.
• Mar 29th 2011, 02:02 AM
CaptainBlack
Quote:

Originally Posted by prasum
find the range of mod(x-1)/x-1

Please use brackets so we do not need to guess that you have left essential brackets out.

CB
• Mar 29th 2011, 02:04 AM
CaptainBlack
Quote:

Originally Posted by prasum
find the range of mod(x-1)/x-1

|x-1|/(x-1)=|x-1|/(sgn(x-1) |x-1|)=sgn(x-1), assuming x is not equal to 1.

CB
• Mar 29th 2011, 02:11 AM
FernandoRevilla
If the OP meant $f(x)=\mod (x-1/x-1)$ then, $f(x)=1$

for all $x\neq 1$ and $\textrm{rg}(f)=\{1\}$ . :)

P.S. Of course, it seems to be mod(x-1)/(x-1).