For $x \in I R, 3 \cos (4 x-5)+4$ lies in the interval
For $x \in I R, 3 \cos (4 x-5)+4$ lies in the interval
- $[1,7]$
- $[4,7]$
- $[0,7]$
- $[2,7]$
Solution
Since, the value of $\cos \theta$ lies between -1 and +1
$
\begin{aligned}
& \text { i.e. }-1 \leq \cos \theta \leq 1 \\
& \therefore \quad-1 \leq \cos (4 x-5) \leq 1 \\
& \Rightarrow \quad-3 \leq 3 \cos (4 x-5) \leq 3 \\
& \Rightarrow \quad 4-3 \leq 3 \cos (4 x-5)+4 \leq 3+4 \\
& \Rightarrow \quad 1 \leq 3 \cos (4 x-5)+4 \leq 7 \\
&
\end{aligned}
$
Asked in: AP EAMCET 2004
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