If f(x)= ( x), thenf(x) f(y)-1 2 [f(x / y)+f(x y)]= - Vidyadip

MCQ

If $f(x)=\cos (\log x)$, then$f(x) f(y)-\frac{1}{2}[f(x / y)+f(x y)]=$

A
-1
B
$\frac{1}{2}$
C
-2
✓
$0$

✓

Answer

Correct option: D.

$0$

(D)
Given, $f (x)=\cos (\log x) \Rightarrow f (y)=\cos (\log y)$
Then, $f (x) . f (y)-\frac{1}{2}\left[ f \left(\frac{x}{y}\right)+ f (x y)\right]$
$=\cos (\log x) \cos (\log y)$
$-\frac{1}{2}\left[\cos \left(\log \frac{x}{y}\right)+\cos (\log x y)\right]$
$=\cos (\log x) \cos (\log y)$
$-\frac{1}{2}[2 \cos (\log x) \cos (\log y)]=0$

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