jee-main 2019 Q79

jee-main · India · session2_08apr_shift2 Exponential Functions Functional Equation with Exponentials

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) $2 f _ { 1 } ( x ) f _ { 1 } ( y )$
(2) $2 f _ { 1 } ( x + y ) f _ { 1 } ( x - y )$
(3) $2 f _ { 1 } ( x ) f _ { 2 } ( y )$
(4) $2 f _ { 1 } ( x + y ) f _ { 2 } ( x - y )$

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) $2 f _ { 1 } ( x ) f _ { 1 } ( y )$\\
(2) $2 f _ { 1 } ( x + y ) f _ { 1 } ( x - y )$\\
(3) $2 f _ { 1 } ( x ) f _ { 2 } ( y )$\\
(4) $2 f _ { 1 } ( x + y ) f _ { 2 } ( x - y )$

Paper Questions

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