f(sin x)= 2sin2x-sinx+1

To analyze the function \( f(\sin x) = 2\sin(2x) - \sin x + 1 \), we can start by simplifying and rewriting the terms. First, we can recall that \( \sin(2x) = 2\sin x \cos x \). Thus, we can rewrite \( f(\sin x) \):

\[ f(\sin x) = 2(2\sin x \cos x) - \sin x + 1 \] \[ = 4\sin x \cos x - \sin x + 1 \]

Now, we can simplify this expression further:

\[ = \sin x (4\cos x - 1) + 1 \]

This gives us a clearer form for \( f(\sin x) \).

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