Sets, Relations and Functions: JEE Main 2022 Mathematics question

JEE Main 2022 · 25 Jun, Morning shift · Q3869

JEE Main 202225 Jun, Morning shiftMathematicsHardSets, Relations and Functions168× since 2002

Let f : N

\to

R be a function such that

f(x + y) = 2f(x)f(y)

for natural numbers x and y. If f(1) = 2, then the value of

\alpha

for which

\sum\limits_{k = 1}^{10} {f(\alpha + k) = {{512} \over 3}({2^{20}} - 1)}

holds, is :