Standard +0.3 This is a straightforward inverse function question requiring students to rearrange y = 1 + 2sin(3x) to make x the subject, then determine the domain from the original range. While it involves arcsin and careful attention to the restricted domain, it follows a standard procedure taught in C3 with no novel problem-solving required, making it slightly easier than average.
The function f(x) is defined by
$$f(x) = 1 + 2\sin 3x, \quad -\frac{\pi}{6} \leqslant x \leqslant \frac{\pi}{6}.$$
You are given that this function has an inverse, \(f^{-1}(x)\).
Find \(f^{-1}(x)\) and its domain. [6]
The function f(x) is defined by
$$f(x) = 1 + 2\sin 3x, \quad -\frac{\pi}{6} \leqslant x \leqslant \frac{\pi}{6}.$$
You are given that this function has an inverse, $f^{-1}(x)$.
Find $f^{-1}(x)$ and its domain. [6]
\hfill \mbox{\textit{OCR MEI C3 Q6 [6]}}