Question

Why is the interval irrelevant?

Answer 1

more information on the way?

Answer 2

So I know the answer is\[\frac{\cot ^{-1}(-y/9)}{ 2 }=x\] but why give the interval if it has no affect on the problem? How is the interval relevant?

Answer 3

because you are writuing the inverse function, so you have to check that in any point of your interval, the inverse function exists. FOr example your interval do not contain a point in which the direct function is infinity

Answer 4

Okay, so if i were to go further and actually find the values resulting from the expression, then I could only include answers that were within the domain?

Answer 5

I think you have to break your interval in sub-intervals in which of the direct function exists

Answer 6

Perl is so smart :)

Answer 7

Thanks!

Answer 8

the interval is important in the original function, since for a function to have an inverse it needs to be one to one (that means it needs to pass the horizontal test)

Answer 9

now
y = -9cot(2x) does not pass the horizontal line test for the unrestricted domain case.

but if you restrict the domain (for some interval of your choosing)
then it does pass the horizontal line test

once it passes the horizontal line test, you can go ahead and find your inverse