A) 1
B) ?1
C) 0
D) \[\pm 1\]
Correct Answer: C
Solution :
\[f(x)=\cos \,(\log x)\] Now let \[y=f(x)\,\,.\,\,f(4)-\frac{1}{2}\,\left[ f\left( \frac{x}{4} \right)+f(4x) \right]\] Þ \[y=\cos \,(\log x).\cos \,(\log 4)-\frac{1}{2}\,\left[ \cos \,\log \,\left( \frac{x}{4} \right)+\cos \,(\log 4x) \right]\] Þ \[y=\cos \,(\log x)\,\cos \,(\log 4)\] \[-\frac{1}{2}\,\left[ \cos \,(\log x-\log 4)+\cos \,(\log x+\log 4) \right]\] Þ \[y=\cos \,(\log x)\,\cos \,(\log 4)-\frac{1}{2}\,\left[ 2\,\cos \,(\log x)\,\cos \,(\log 4) \right]\] Þ \[y=0\].
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