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Let \( f(x)=a^{x}(a0) \) be written as \( f(x)=f_{1}(x)+f_{2}(x) \), where \( f_{1}(x) \) is an even function of \( f_{2}(\mathrm{x}) \) is an odd function. Then \( f_{1}(\mathrm{x}+\mathrm{y})+f_{1}(\mathrm{x}-\mathrm{y}) \) equals [JEEMain \( 2019( \) April \( \left.)\right] \)
\( \mathrm{P} \)
W.
(a) \( 2 f_{1}(\mathrm{x}) f_{1}(\mathrm{y}) \)
(b) \( 2 f_{1}(\mathrm{x}) f_{2}(\mathrm{y}) \)
(c) \( 2 f_{1}(x+y) f_{2}(x-y) \)
(d) \( 2 f_{1}(x+y) f_{1}(x-y) \)
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