Let S = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Define f: S → S as f(n) = \ 2n, if n = 1,2,3,4,5 2n - 11, if n = 6,7,8,9,10.. Let g: S → S be a function such that fog(n) = \ n + 1, if n is odd n - 1, if n is even.. Then g(10)g(1) + g(2) + g(3) + g(4) + g(5)) is equal to _ _ _ _ _ _ _.

Sets, Relations and Functions: JEE Main 2022 Mathematics question

JEE Main 2022 · 27 Jun, Evening shift · Q35

JEE Main 202227 Jun, Evening shiftMathematicsHardSets, Relations and Functions168× since 2002

Let S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Define f : S

\to

S as

f(n) = \left\{ {\matrix{ {2n} & , & {if\,n = 1,2,3,4,5} \cr {2n - 11} & , & {if\,n = 6,7,8,9,10} \cr } } \right.

. Let g : S

\to

S be a function such that

fog(n) = \left\{ {\matrix{ {n + 1} & , & {if\,n\,\,is\,odd} \cr {n - 1} & , & {if\,n\,\,is\,even} \cr } } \right.

. Then

g(10)g(1) + g(2) + g(3) + g(4) + g(5))

is equal to _____________.

Your answerType your answer. Integers and decimals are accepted.