Let f(x)=a^ x (a>0) be written as f(x)=f_ 1 (x)+f_ 2 (x) , where f_ 1 (x) is an even…

Mathematics · JEE Main · NTA ExamsSets, Relations and Functions

Let \(f(x)=a^{x}(a>0)\) be written as \(f(x)=f_{1}(x)+f_{2}(x)\), where \(f_{1}(x)\) is an even function and \(f_{2}(x)\) is an odd function. Then \(f_{1}(x+y)+f_{1}(x-y)\) equals
  1. \(2 f_{1}(x+y) f_{2}(x-y)\)
  2. \(2 f_{1}(x+y) f_{1}(x-y)\)
  3. \(2 f_{1}(x) f_{2}(y)\)
  4. \(2 f_{1}(x) f_{1}(y)\)

Answer

(D) 2 f_ 1 (x) f_ 1 (y)

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