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)$
D
$ \text{R}$

✓

Answer

$ \text{R}$

Solution:

Given,

function is $ \text{f}(\text{x}) = \frac{1}{(2 -\cos 3\text{x})}$

Since $ -1 \leq \cos \text{3x} \leq1$ for all$\text{ x }∈\text{R}$

So,$ -1 \leq 2 \cos \text{3x} \leq1$for all$\text{ x }∈\text{R}$

⇒ $\text{f}(\text{x})$ is defined for all$\text{ x }∈\text{R}$

So, domain of f(x) is R.

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