Functions Question 610
Question: If $ f(x)=\cos (\log x) $ , then the value of $ f(x).f(4)-\frac{1}{2}
[ f( \frac{x}{4} )+f(4x) ] $ [Kurukshetra CEE 1998]
Options:
A) 1
B) ?1
C) 0
D) $ \pm 1 $
Show Answer
Answer:
Correct Answer: C
Solution:
$ f(x)=\cos ,(\log x) $ Now let $ y=f(x).f(4)-\frac{1}{2},[ f( \frac{x}{4} )+f(4x) ] $
Þ $ y=\cos ,(\log x).\cos ,(\log 4)-\frac{1}{2},[ \cos ,\log ,( \frac{x}{4} )+\cos ,(\log 4x) ] $
Þ $ y=\cos ,(\log x),\cos ,(\log 4) $ $ -\frac{1}{2},[ \cos ,(\log x-\log 4)+\cos ,(\log x+\log 4) ] $
Þ $ y=\cos ,(\log x),\cos ,(\log 4)-\frac{1}{2},[ 2,\cos ,(\log x),\cos ,(\log 4) ] $
Þ $ y=0 $ .
BETA
