Question

Are the growths of the functions f(x) = sinx and g(x) = -sin(-x) the same or different

Answer 1

To analyze the growths of the functions \( f(x) = \sin(x) \) and \( g(x) = -\sin(-x) \), we should first simplify \( g(x) \).

Using the property of the sine function, we know that \( \sin(-x) = -\sin(x) \). Therefore:

\[
g(x) = -\sin(-x) = -(-\sin(x)) = \sin(x)
\]

So,

\[
g(x) = \sin(x)
\]

Now we can see that:

- \( f(x) = \sin(x) \)
- \( g(x) = \sin(x) \)

Both functions are identical, which means they have the same growth behavior.

Thus, the growths of the functions \( f(x) \) and \( g(x) \) are the same.