Question

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

Answer 1

To determine whether the graphs of the functions \( f(x) = \sin x \) and \( g(x) = -\sin(-x) \) are the same or different, we can analyze the function \( g(x) \).

First, let's simplify \( g(x) \):

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

Using the property of the sine function that states \( \sin(-x) = -\sin(x) \), we can rewrite \( g(x) \):

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

Thus, we see that:

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

Since both \( f(x) \) and \( g(x) \) are equal to \( \sin x \), the graphs of the functions \( f(x) \) and \( g(x) \) are indeed the same.

In conclusion, the graphs of \( f(x) = \sin x \) and \( g(x) = -\sin(-x) \) are the same.