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Let f (x) = a ^ x ( a gt 0 ) b...

Let ` f (x) = a ^ x ( a gt 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 :

A

` 2 f _ 1 (x ) f _ 2 (x ) `

B

` 2 f _ 1 (x + y) f _ 2 ( x - y ) `

C

`2 f _ 1 ( x + 1 ) f _ 1 (x - y ) `

D

`2 f_ 1 ( x ) f _ 1 ( y) `

Text Solution

Verified by Experts

` f _ 1 (x ) = ( a ^ x + a ^( -x ))/( 2 ) rArr f _ 1 (x + y ) + f _ 1 ( x - y ) `
` = 2 f _ 1 ( x ) f _ 1 ( x ) `
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