How to invert sign/signum function?

Question

I have problem like this one: there is a relation like,
y=sgn(x)*(x-2); so here y is expressed as a function of x.
I want to express x as a function of y. How to do that? sgn(x)=|x|/x, (x not equal to zero).

Can you also tell me about any website other than yahoo answers where I can discuss my doubts concerning higher maths/physics?

Answer 1

THE QUESTION WHICH HAS BEEN STATED HAS TO BE BROKEN IN 3 FOLDS
1) X<0;
....SGN(X) = (-1)
....SO
....y = (2 - X)
.....X= 2-y
2) X= 0
....SGN(X) = (0)
....SO
....Y= 0
3) X>0
....SGN(X) = (1)
....SO
....Y=X-2
....X=Y+2


SO THE ANSWER IS

---- X = 2-Y ; X<0
---- Y=0 ; X=0
---- X=Y+2 ; X>0

Answer 2

The signum function, sgn (x), is not one to one – in fact, obviously very much not so!
So it cannot be inverted, at least, not uniquely. Nor can the example function quoted; nor can a quadratic function, nor a trigonometric function. However, these last two can guide us how to proceed.

Suppose that y = sgn (x) * (x - 2),
= x - 2, x > 0, or
= 0 , x = 0, or
= 2 - x, x < 0
(Consider the graph)
We have:
for y ≤ -2, there are no solutions;
for -2 < y < 0, or 0 < y < 2, a unique solution:
x = y + 2;
for y = 0, two solutions: 0 or 2;
for y ≥ 2, two solutions:
x = y + 2, or x = -(y + 2).
Does this help?

Answer 3

Signum Function

Answer 4

The given function does not have a well-defined inverse. To convince yourself of this, sketch a graph.

I recommend The Student Room for discussing academic work; its Maths forum in particular is very good.

Answer 5

signum function has three values for infinite inputs
so from these you can not retrace the inputs .
hence the function does not have any inverse

Answer 6

I gave it a try.... I also struggle with how to invert |x|.

One line of thought is
if y = |x|,
then x = +- y
or x = +y & x = -y

Let me know when you get the answer.

Answer 7

take the first equation a1= 2 + 3/2 a2 and isolate a2 a1 - 2 = 3/2 a2 (2(a1-2))/3) = a2 -4/3 + 2/3 a1 = a2 and there you go