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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
Let $f(x)=\dfrac{1}{7-\sin5x}$ be a function defined on $\mathbb{R}$.
Then the range of the function $f(x)$ is equal to:
Solution
Since $-1 \le \sin 5x \le 1$$\Rightarrow 7-1 \le 7-\sin 5x \le 7+1$
$\Rightarrow 6 \le 7-\sin 5x \le 8$
Now take reciprocal (all positive, so inequality reverses order accordingly): $\Rightarrow \frac{1}{8} \le \frac{1}{7-\sin 5x} \le \frac{1}{6}$
Hence, range is $ \boxed{\left[\frac{1}{8},\frac{1}{6}\right]} $
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