Q. If $f:R \rightarrow R$ and is defined by $f(x) = \frac{1}{2 - \cos{3x}}$ for each $x \in R$, then the range f $f$ is
A) (1/3, 1)
B) [1/3, 1]
C) (1, 2)
D) [1, 2]
Explanation
(b)
Since, $- 1 \leq \cos{3x \leq 1}$
$\Rightarrow \ \ 1 \leq - \cos{3x\ \leq - 1}$
$\Rightarrow \ 3 \leq 2 - \cos{3x\ \leq 1}$
$\Rightarrow \ \frac{1}{3} \leq \frac{1}{2 - \cos{3x}} \leq 1$
$\therefore$ Range of $f$ is $\left\lbrack \frac{1}{3},\ 1 \right\rbrack$.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.