Question

how can we find the domain and range of Sin^{-1} (x-y)

Answer 1

Something is missing in this problem. There should be an equation and there isn't one here.

Also is that sine inverse or arc sine as in:
\[\Large \sin ^{-1}(x - y)\]?

Answer 2

yes it is like that

Answer 3

i wanted to know the method of finding domain and range of inverse functions....

Answer 4

range is always [-1,1] of arc sin

Answer 5

but here 2 variables are involved

Answer 6

not to worry.... arc sin is always confined between -1 and 1 and domain is real

Answer 7

real no.***

Answer 8

The sine function has a minimum value of -1 and a maximum value of +1. So the (x - y) here has to be confined to [-1, 1]. That is all we can say from the data.

Answer 9

Normally when they ask for domain and range it means what are the allowed values for x and what are the allowed values for y. Here all you can say is:
-1 <= (x - y) <= 1

Answer 10

If sin(A) = B then we can be sure B has to be: -1 <= B <= 1
So A = arc sin(B).
We can only take arc sin when the value is between [-1, 1]

So in this problem: -1 <= (x - y) <= 1

I don't know what else they are expecting.

Answer 11

thanks...

Answer 12

sure.

Answer 13

The allowed values for x and y fall in between those two straight lines. So in reality each of x and y can be from -infinity to +infinity as long as -1 <= (x - y) <= 1

So there is a constraint equation. While each of a and y can take any value, as soon as one is defined the other is constrained by -1 <= (x - y) <= 1