Let f(x)=ax(a>0) be written as f(x)=f1(x)+f2(x), where f1(x) is an even function and f2(x) is an odd function. Then f1(x+y)+f1(x−y) equals :
A
2f1(x)f1(y)
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B
2f1(x+y)f1(x−y)
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C
2f1(x)f2(y)
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D
2f1(x+y)f2(x−y)
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Solution
The correct option is A2f1(x)f1(y) Every function f(x) can be represented as f(x)=f(x)+f(−x)2+f(x)−f(−x)2, where f(x)+f(−x)2 is even function and f(x)−f(−x)2 is odd function.