The range of values of the function f ( x ) = 1 2 - 3 x is - Vidyadip

MCQ

The range of values of the function $f\left( x \right) = \frac{1}{{2 - 3\sin x}}$ is

A
$\left[ { - 1,\frac{1}{5}} \right]$
B
$\left[ { - 1,5} \right]$
✓
$\left( { - \infty , - 1} \right] \cup \left[ {\frac{1}{5},\infty } \right)$
D
$\left( { - \infty ,\frac{1}{5}} \right] \cup \left[ {1,\infty } \right)$

✓

Answer

Correct option: C.

$\left( { - \infty , - 1} \right] \cup \left[ {\frac{1}{5},\infty } \right)$

c
$-3 \leq 3 \sin x \leq 3$

$-1 \leq 2-3 \sin x \leq 5$

$\frac{1}{2-3 \sin x} \in(-\infty,-1] \cup\left[\frac{1}{5}, \infty\right)$

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