The domain of the function f (x) = 1 (2 - 3x) is: - Vidyadip

MCQ

The domain of the function $ \text {f} (\text{x}) = \frac{1}{(2 -\cos 3\text{x})}$ is:

A
$ \Big (\frac{1}{3}, 1\Big)$
B
$ \Big (\frac{1}{3}, 1\Big)$
C
$ \Big (\frac{1}{3}, 1\Big)$
✓
$ \text{R}$

✓

Answer

Correct option: D.

$ \text{R}$

Given,
function is $ \text{f}(\text{x}) = \frac{1}{(2 -\cos 3\text{x})}$
Since $ -1 \leq \cos \text{3x} \leq1$ for all$\text{ x }\in \text{R}$
So,$ -1 \leq 2 \cos \text{3x} \leq1$for all$\text{ x }\in \text{R}$
$\Rightarrow \text{f}(\text{x})$ is defined for all$\text{ x }\in \text{R}$
So, domain of $f(x)$ is $R.$

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