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Question

if f(x)=9x9x+3 then f(11996)+f(21996)+.........

A
997
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B
997.5`
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C
998
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D
998.5
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Solution

The correct option is A 997.5`
Observing that the terms to be summed are of the form f(x)from one end
Putting x as (1x) the other

Putting f(1x) we get,

f(1x)=33+9x

Thus f(x)+f(1x)=1

Coupling the terms

f(11996)+f(19951996)=1

Similarly f(21996)+f(19941996)=1

Now, 997 such couples exist. Which gives a sum 997.

and remaining term, f(9981996)=f(12), Solving =12

thus Sum =997+0.5=997.5


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