To express the function \( f(x) = -2\sin(x - \pi) + 3 \) as a cosine function, we can use the relationship between sine and cosine. The sine function can be expressed in terms of cosine like this:
\[ \sin(x - \pi) = -\cos(x) \]
Now, substitute this into the function:
\[ f(x) = -2\sin(x - \pi) + 3 = -2(-\cos(x)) + 3 \]
This simplifies to:
\[ f(x) = 2\cos(x) + 3 \]
Therefore, the function \( f(x) = -2\sin(x - \pi) + 3 \) can be rewritten as:
\[ f(x) = 2\cos(x) + 3 \]