Functions 2 Question 10
11. If $f(x)=\cos (\log x)$, then $f(x) \cdot f(y)-\frac{1}{2} f \frac{x}{y}+f(x y)$ has the value
(1983, 1M)
(a) -1
(b) $\frac{1}{2}$
(c) -2
(d) None of these
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Answer:
Correct Answer: 11. (a, c)
Solution:
- Given, $f(x)=\cos (\log x)$
$\therefore f(x) \cdot f(y)-\frac{1}{2} f \frac{x}{y}+f(x y)$
$=\cos (\log x) \cdot \cos (\log y)-\frac{1}{2}[\cos (\log x-\log y)$
$+\cos (\log x+\log y)]$
$=\cos (\log x) \cdot \cos (\log y)-\frac{1}{2}[(2 \cos (\log x) \cdot \cos (\log y)]$ $=\cos (\log x) \cdot \cos (\log y)-\cos (\log x) \cdot \cos (\log y)=0$
