Question

$A=\{x:\frac{\pi }{6}\le x\le \frac{\pi }{3}\}$ and $f\left(x\right)=\cos x$ then

• A. $f\left(A\right)=[\frac{1}{2},\frac{\sqrt{3}}{2}]$
• B. $f\left(A\right)=[2,\sqrt{3}]$
• C. $f\left(A\right)=[\frac{1}{2},1]$
• D. $[\frac{\sqrt{3}}{2},1]$

Answer 1

Answer: (A)

$f\left(A\right)=[\frac{1}{2},\frac{\sqrt{3}}{2}]$

$f\left(x\right)=\cos x$ is decreasing in $A$.
$\therefore f\left(\frac{\pi }{6}\right)=\frac{\sqrt{3}}{2}$ & $f\left(\frac{\pi }{3}\right)=\frac{\cos \pi }{3}$

$=\frac{1}{2}$
$\therefore f\left(A\right)=[\frac{1}{2},\frac{\sqrt{3}}{2}]$