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1.Relation and Function
medium
જો $f(x) = \cos (\log x)$, તો $f(x)f(y) - \frac{1}{2}[f(x/y) + f(xy)] = $
A
$ - 1$
B
$\frac{1}{2}$
C
$ - 2$
D
એકપણ નહી.
(IIT-1983)
Solution
(d) Given $f(x) = \cos \,(\log x)\,\, \Rightarrow \,f(y) = \cos \,(\log y)$
Then $f(x).f(y) – \frac{1}{2}\left[ {f\left( {\frac{x}{y}} \right) + f(xy)} \right]$
$ = \cos \,(\log x)\cos \,(\log y) – \frac{1}{2}\left[ {\cos \left( {\log \frac{x}{y}} \right) + \cos \,(\log xy)} \right]$
$ = \cos \,(\log x)\,\cos \,(\log y) – \frac{1}{2}\,[2\cos \,(\log x)\cos \,(\log y)]= 0.$
Standard 12
Mathematics
