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General Solution of Trigonometric Equation

The domain of...

Question

The domain of $f (x) = {sin}^{- 1} (\frac{x - 4}{3}) + log (2 - x)$ is

A

[1, 4]

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B

[1, 2)

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C

[1, 3)

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D

[0, 1)

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Solution

The correct option is A $[1, 2)$
We know that,

$- 1 \leq sin x \leq 1$

For $f$ to be defined,

$- 1 \leq \frac{x - 4}{3} \leq 1$ and $2 - x > 0$
$\Rightarrow - 3 \leq x - 4 \leq 3$ and $x < 2$
$\Rightarrow 1 \leq x \leq 7$ and $x < 2$
From above required domain is $[1, 2)$

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General Solution of Trigonometric Equation

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