Q.

If fx+gx=e-x where fx is an even function and gx is odd function, then fx=

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a

ex-ex2

b

ex2

c

ex+ex2

d

ex2

answer is B.

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Detailed Solution

Given fx+gx=e-x            ..... (1)

Given that fx is even function, so that f-x=fx and gx is odd function, so that g-x=-gx

Replace x by -x in the given functional equation 

Hence, 

 f-x+g-x=exfx-gx=ex       ...... (2)

By adding both (1) and (2)

We get 

2fx=ex+e-x

Therefore, fx=ex+e-x2

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