MCQ
જો $f(x)=\frac{2^x+2^{-x}}{2},$ તો $f(x+y)\ \ f(x-y)=$ ...............
- ✓$\frac{1}{2} [f(2x)+f(2y)]$
- B$\frac{1}{4} [f(2x)+f(2y)]$
- C$\frac{1}{2} [f(2x)-f(2y)]$
- D$\frac{1}{4} [f(2x)-f(2y)]$
$f(x)=\frac{2^x+2^{-x}}{2}$
$\therefore f(x+y)= \frac{2^{x+y}+2^{-x-y}}{2}$ અને $f(x-y) = \frac{2^{x-y}+2^{-x+y}}{2}$
$\therefore f(x+y) \ . \ f(x-y) = \left(\frac{2^{x+y}+2^{-x-y}}{2}\right)\ \left(\frac{2^{x-y}+2^{-x+y}}{2}\right)\ $
$=\frac{1}{2}\left[\frac{2^{2x}+2^{-2x}}{2}+\frac{2^{2y}+2^{-2y}}{2}\right]$
$=\frac{1}{2} [f(2x)+f(2y)]$
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