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

✓

Answer

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

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