Methods2023 Exam 2 Section A · Q20CAS active1 mark

Domain where both composite functions exist

Let $f(x) = \log_e\left(x + \frac{1}{\sqrt{2}}\right)$ .

Let $g(x) = \sin(x)$ where $x \in (-\infty, 5)$ .

The largest interval of $x$ values for which $(f \circ g)(x)$ and $(g \circ f)(x)$ both exist is

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\left(-\frac{1}{\sqrt{2}}, \frac{5\pi}{4}\right)

\left[-\frac{1}{\sqrt{2}}, \frac{5\pi}{4}\right)

\left(-\frac{\pi}{4}, \frac{5\pi}{4}\right)

\left[-\frac{\pi}{4}, \frac{5\pi}{4}\right]

\left[-\frac{\pi}{4}, -\frac{1}{\sqrt{2}}\right]

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