If f(x)=| x|, then f (3 4 ) is - Vidyadip

MCQ

If $f(x)=|\cos x|$, then $f\left(\frac{3 \pi}{4}\right)$ is

A
$1$
B
$-1$
C
$\frac{-1}{\sqrt{2}}$
✓
$\frac{1}{\sqrt{2}}$

✓

Answer

Correct option: D.

$\frac{1}{\sqrt{2}}$

$f(x)=|\cos x|$
At$\frac{\pi}{2} < x < \pi, \cos x < 0$
$\therefore|\cos x|=-\cos x$
$\Rightarrow f(x)=-\cos x$
$\therefore f\left(\frac{3 \pi}{4}\right)$
$=-\cos \left(\frac{3 \pi}{4}\right)$
$=-\cos \left(\pi-\frac{\pi}{4}\right)$
$=\cos \frac{\pi}{4}$
$=\frac{1}{\sqrt{2}} [\because \cos (\pi-\theta)=-\cos \theta]$

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