Functions Question 388
Question: If $ f(x)=\frac{2^{x}+{2^{-x}}}{2} $ , then $ f(x+y).f(x-y) $ is equal to
Options:
A) $ \frac{1}{2}[f(x+y)+f(x-y)] $
B) $ \frac{1}{2}[f(2x)+f(2y)] $
C) $ \frac{1}{2}[f(x+y).f(x-y)] $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
[b] $ f(x+y).f(x-y) $ $ =\frac{{2^{x+y}}+{2^{-x-y}}}{2}.\frac{{2^{x-y}}+{2^{-x+y}}}{2} $ $ =\frac{2^{2x}+2^{2y}+{2^{-2x}}+{2^{-2y}}}{2\times 2} $ $ =\frac{1}{2}[ \frac{2^{2x}+{2^{-2x}}}{2}+\frac{2^{2y}+{2^{-2y}}}{2} ] $ $ =\frac{1}{2}[f(2x)+f(2y)] $
BETA
