modulus function????

Question

f(x)=IxI.......im really confused with this...in my course book it is given that x becomes the positive on taking mod....but sometimes ,my teacher takes it both positive and negative....can anyone please clarify my doubt???

Answer 1

The modulus means that all positive value are taken as positive, i.e x=1, f(x)=1 , x=99.6636, f(x) = 99.6636.

The modulus also means that all negative values are effectively taken as the positive value (in effect the minus sign is ignored)

i.e x=-1, f(x) =1, x=- 99.663, f(x) = 99.6636.

So in effect the function has two possibilities , with x=1 or -1, have a modulus of 1. Hope that helps.

So that x<1 , f(x) = x

if x>1, f(x) = x

Answer 2

Errmmmm........ Now you've got *me* confused. Are you talking about the absolute value (abs(x) or |x|) or are you talking about the 'modulus' of an integer with respect to another integer (also sometimes called the 'remainder' function). I'm going to guess it really is the modulus and go from there.

The modulus (mod) function is the 'remainder' of an iunteger after division. For example, 17(mod 5) = 2. There are a lot of reasons for studying modular arithmetic (especially if the modulus is a prime number), but your question was how can a modulus be negative.

Look at the above example, 17(mod 5). Now 17/5 vertainly has a remainder of 2, but it can also be said that 17/5 has a remainder of -3 (that is 20 - 3 = 17 and
(20 - 3)/5 = 0 with a -3 remainder. And it's kinda useful sometimes to be able to use it this way.

HTH ☺


Doug

Answer 3

Think of it this way, keeping with real numbers, think of them as vector quantities, that is they have both a magnitude and a direction..
The magnitude is basically the value we write in digits, the direction is defined by the sign associated with the magnitude, the modulus function basically maps any real a onto its magnitude which is always positive, then,
I-6I = 6
I-1/2I = 1/2
I7I = 7

Hope this helps!

Answer 4

The functio f(x) must always be POSITIVE whatever the value of x. So if x is positive then it's clear that f(x) = x is also positive.

If x is negative and f(x) must be positive then you must multiply every negative x by -1 to obtain the value of the function for negative values of x.

Look at it this way


f(x) = x ; if x >= 0

f(x) = -x; if x < 0

Answer 5

x doesnt become positive...

even after taking mod on x, x doesnt change value... it will still be positive or negative...

ex: if x = -2, |x| = 2... but x is still -2 (negative)

Answer 6

I'm used to the notation |x| meaning the absolute value, so |x| = |-x| for all x.