Let c, k R. If f(x) = (c + 1)x² + (1 - c²)x + 2k and f(x + y) = f(x) + f(y) - xy, for all x, y R, then the value of |2(f(1) + f(2) + f(3) +...... + f(20))| is equal to _ _ _ _ _ _.

Sets, Relations and Functions: JEE Main 2022 Mathematics question

JEE Main 2022 · 29 Jun, Morning shift · Q38

JEE Main 202229 Jun, Morning shiftMathematicsMediumSets, Relations and Functions168× since 2002

Let c, k

\in

R. If

f(x) = (c + 1){x^2} + (1 - {c^2})x + 2k

and

f(x + y) = f(x) + f(y) - xy

, for all x, y

\in

R, then the value of

|2(f(1) + f(2) + f(3) + \,\,......\,\, + \,\,f(20))|

is equal to ____________.

Your answerType your answer. Integers and decimals are accepted.