JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 26 July 2022, Shift 1, Maths Q1

Question 1 of 90 in this shift, Maths question 1 of 30, Section A.

Let

f : \mathbf{R} \rightarrow \mathbf{R}

be a continuous function such that

f\,(3x) - f\,(x) = x

. If

f\,(8) = 7

, then

f\,(14)

is equal to :

(1) $4$
(2) $10$ Official answer
(3) $11$
(4) $16$

Official answer

Option 2

NTA final key.

Chapter: Continuity and Differentiability
Topic: Continuity and Differentiability
Idea tested: Differentiability via Functional Equations

Same idea in other shifts

Asked 10× in all

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4 Aug 2021, Shift 2 · Q67Let $f:\mathbb{R}\to\mathbb{R}$ be twice differentiable and satisfy $f(x+y)=f(x)+f(y)$ . If $f'(0)=1$ , then which of the following is true?EasySingle correct
26 Feb 2021, Shift 1 · Q74Let $f$ be any function defined on $\mathbf{R}$ and let it satisfy the condition :…MediumSingle correct
18 Mar 2021, Shift 2 · Q90Let $f:\mathbb{R}\to\mathbb{R}$ satisfy the equation $f(x+y)=f(x)\cdot f(y)$ for all $x, y\in\mathbb{R}$ and $f(x)\neq0$ for any…MediumNumerical value
4 Sep 2020, Shift 1 · Q73Suppose a differentiable function $f(x)$ satisfies the identity $f(x+y) = f(x) + f(y) + xy^2 + x^2y$ , for all real $x$ and $y$ . If…MediumNumerical value

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.