Question

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

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

Answer 1

Answer: (A)

$[1,7]$

We know that $-1\le \cos x\le 1$

Hence

$-1\le cos(4x-5)\le 1$

Multiply both the sides by 3 and add 4 to either side of the inequality to get the equation required
$1\le 3cos(4x-5)+4\le 7$