Introduction to real valued functions

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Question

The domain of definition of $f (x) = \log_{x} \cos x$ , is $(0, π / 2) - {k}$ then k is

Moderate

Solution

For $f (x)$ to be real, we must have
$\cos x > 0, x > 0$ and $x \neq 1$
$\Rightarrow - π / 2 < x < π / 2, x > 0$ and $∣ x \neq 1 \Rightarrow x \in (0, π / 2) - {1}$
Hence, domain $(f) = (0, π / 2) - {1}$

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