InterviewSolution
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InterviewSolution
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`f(x) = 9^x/ ( 1 + 9^x)` then value of `f(1/2015) + f(2/2015) .......+ f(4029/2015)`A. 1007B. `(4029)/(2)`C. 2014D. 2015 |
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Answer» Correct Answer - D We have `f(x) = (9^(x))/(9^(x)+9)` `therefore " " f(2-x) = (9^(x-2))/(9^(2-x)+9)` So,`f(x) +f(2-x)=(9^(x))/(9^(x)+9) +(9^(x-2))/(9^(2-x) +9) = (9^(x))/(9^(x)+9)+(9)/(9+9^(x)) =1` `rArr f(x) + f(2-x) = 1` `therefore " "f{(1)/(2015)}+f((2)/(2015)) +((3)/(2015))+......+f((4029)/(2015))` `= {f((1)/(2015)) +f((4029)/(2015))}+{f((2)/(2015))+f((4028)/(2015))}+.....+{f((20+f((2014)/(2015))+f((2016)/(2015))}+f((2015)/(2015))` `={1 +1+....+1(2014 "times")} +f(1) = 2014 +(1)/(2) = (4029)/(2)` |
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