JEE Main 2019 — Functions Question with Solution
From: JEE Main 2019 (Online) 9th April Morning Slot
Question
Let where the function
ƒ satisfies
ƒ(x + y) = ƒ(x)ƒ(y) for all natural numbers x, y and ƒ(1) = 2. then the natural number 'a' is
ƒ(x + y) = ƒ(x)ƒ(y) for all natural numbers x, y and ƒ(1) = 2. then the natural number 'a' is
Choose an option
Show full solutionCorrect option: D
Correct answer
D3
Step-by-step explanation
Given ƒ(1) = 2
and ƒ(x + y) = ƒ(x)ƒ(y)
When x = 1 and y = 1 then,
ƒ(1 + 1) = ƒ(1)ƒ(1)
f(2) = (f(1))2 = 22
Also when x = 2 and y = 1 then,
ƒ(2 + 1) = ƒ(2)ƒ(1)
f(3) = 23
Similarly f(4) = 24
.
.
.
.
f(x) = 2x
f(a + k) = 2a + k
Now given,
=
=
=
=
= 3
and ƒ(x + y) = ƒ(x)ƒ(y)
When x = 1 and y = 1 then,
ƒ(1 + 1) = ƒ(1)ƒ(1)
f(2) = (f(1))2 = 22
Also when x = 2 and y = 1 then,
ƒ(2 + 1) = ƒ(2)ƒ(1)
f(3) = 23
Similarly f(4) = 24
.
.
.
.
f(x) = 2x
f(a + k) = 2a + k
Now given,
=
=
=
=
= 3
Practice this on the real CBT interface
Solve this JEE Main question (and the rest of the Functions chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.
Solve interactively →About this question
This is a previous-year question from JEE Main 2019, covering the Functions chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.