Q69 / 160 · TS EAMCET 2004 · Mathematics

For $x \in I R, 3 \cos (4 x-5)+4$ lies in the interval

  • Correct answer
    A
    $[1,7]$
  • B
    $[4,7]$
  • C
    $[0,7]$
  • D
    $[2,7]$

Solution

Since, the value of $\cos \theta$ lies between -1 and +1 $$ \begin{aligned} & \text { i.e. }-1 \leq \cos \theta \leq 1 \\ & \therefore \quad-1 \leq \cos (4 x-5) \leq 1 \\ & \Rightarrow \quad-3 \leq 3 \cos (4 x-5) \leq 3 \\ & \Rightarrow \quad 4-3 \leq 3 \cos (4 x-5)+4 \leq 3+4 \\ & \Rightarrow \quad 1 \leq 3 \cos (4 x-5)+4 \leq 7 \\ & \end{aligned} $$

Hence, the correct answer is option: 'A'.

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