Question

Find domain and inverse domain of the function.
f(x)=9sin(8x-1) Explain please (:

Answer 1

The domain of the sin function is R, all the real numbers. What do you mean by inverse domain of the function? English is not my first language, so I assume it's the domain of the inverse function.

Answer 2

It is! The domain of the inverse function

Answer 3

The domain becomes the image and the other way round is also true. Let's check the image of 9sin(8x-1): We have that IM sin(x) is\[-1 \le x \le 1\] Therefore, multiplying the IM by 9 we have that \[-9 \le x \le 9\]Applying that little rule, the domain of its inverse is \[-9 \le x \le 9\]

Answer 4

It said the domain for the first function was (-∞,∞)

Answer 5

Yes. It is true for any sin(x) function. By saying "All real numbers" I meant (-∞,∞).
For the inverse function, the image of 9sin(8x-1) becomes the arcsin domain.

Answer 6

Thank you! (: