Question

Given f(x)=sin(x) state the domain of so that f is injective.

Answer 1

I think the answer is every multiple of \[(-\pi/2, \pi/2)\] but Im not sure

Answer 2

and those should be closed brackets, not open.

Answer 3

That simply means that you want to find any interval where sin(x) doesn't repeat. Since a function that is injective does only take on a single value for a given x. An example of such an interval is \([-\frac{\pi}{2},\frac{\pi}{2})\) or \([0,1]\). Think of it that any line x=constant should only cross it's graph once.

Answer 4

thanks, thought so, but wasn't sure!