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Question

If fx=4x4x+2, then f197+f297+.......+f9697 is equal to:


A

1

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B

48

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C

-48

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D

-1

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Solution

The correct option is B

48


Explanation for the correct option.

Step 1: Find the value of f(x)+f(1-x).

fx=4x4x+2, so

f1-x=41-x41-x+2=44x44x+2=44+24x=24x+2

Now,

f(x)+f(1-x)=4x4x+2+24x+2=1

Step 2: Find the value of f197+f297+.......+f9697.

f197+f9697=f197+f1-197=1byfx+f1-x

Similarly,

f297+f9597=f297+f1-297=1

So, in f197+f297+.......+f9697, there will be total 48 such groups whose sum will be 1.

Therefore,

f197+f297+.......+f9697=148=48

Hence, option B is correct.


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