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Question

If f(x)andg(x) are two functions of x such that f(x)+g(x)=ex and f(x)g(x)=e-x, then:


A

f(x) is odd, g(x) is odd

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B

f(x) is even, g(x) is even

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C

f(x) is even, g(x) is odd

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D

f(x) is odd, g(x) is even

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Solution

The correct option is C

f(x) is even, g(x) is odd


Explanation for the correct option.

Step 1: Find the value of fx.

f(x)+g(x)=ex...(1)

f(x)g(x)=e-x....2

By adding 1 and 2, we get

2fx=ex+e-xfx=ex+e-x2

Step 2: Find the value of gx.

Substituting the value of fx in 2, we get

gx=ex+e-x2-e-x=ex+e-x-2e-x2=ex-e-x2

Step 3: Find fx and gx are odd or even.

f-x=e-x+ex2=fx

So, fx is even function.

g-x=e-x-ex2=-gx

So, gx is an odd function.

Hence, option C is correct.


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