JEE Main 2019 — Functions Question with Solution
From: JEE Main 2019 (Online) 10th January Evening Slot
Question
Let N be the set of natural numbers and two functions f and g be defined as f, g : N N such that
f(n) = \left\{ {\matrix{ {{{n + 1} \over 2};} & {if\,\,n\,\,is\,\,odd} \cr {{n \over 2};} & {if\,\,n\,\,is\,\,even} \cr } \,\,} \right.;
and g(n) = n ( 1)n.
Then fog is -
f(n) = \left\{ {\matrix{ {{{n + 1} \over 2};} & {if\,\,n\,\,is\,\,odd} \cr {{n \over 2};} & {if\,\,n\,\,is\,\,even} \cr } \,\,} \right.;
and g(n) = n ( 1)n.
Then fog is -
Choose an option
Show full solutionCorrect option: B
Correct answer
Bonto but not one-one
Step-by-step explanation
f(x) = \left\{ {\matrix{
{{{n + 1} \over 2};} & {if\,\,n\,\,is\,\,odd} \cr
{{n \over 2};} & {if\,\,n\,\,is\,\,even} \cr
} \,\,} \right.;
g(x) = n ( 1)n
f(g(n)) =
many one but onto
g(x) = n ( 1)n
f(g(n)) =
many one but onto
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