What is the range of the function $f (x) = 2 sin (3 x) + 1$ ?

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Let $f (x) = 4 - x^{2}$ and $g (x) = 2 x - 1$ . The maximal domain of the composite function $f (g (x))$ is:
The transformation $T : R^{2} \to R^{2}$ maps $(x, y)$ to $(x^{'}, y^{'})$ where $x^{'} = 3 x - 1$ and $y^{'} = - 2 y + 4$ . If the image curve…
Find the rule and domain of the inverse function $f^{- 1} (x)$ for $f : [2, \infty) \to R, f (x) = (x - 2)^{2} + 3$ .
The graph of $y = \frac{a}{x - b} + c$ has asymptotes at $x = 3$ and $y = - 2$ , and passes through the origin $(0, 0)$ . What is the value of…
Determine the period and amplitude of the function $h (t) = 5 - 3 cos (\frac{π t}{4})$ .
For the function $f (x) = x^{3} - 3 k x^{2} + 9 x - 1$ to have strictly no stationary points, the real parameter $k$ must satisfy: