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Saturday, 31 October

JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 18 March 2021, Shift 2, Maths Q76

Question 76 of 90 in this shift, Maths question 16 of 30, Section A.

Let f:R−{3}→R−{1}f:\mathbb{R}-\{3\}\to\mathbb{R}-\{1\} be defined by f(x)=x−2x−3f(x)=\frac{x-2}{x-3}. Let g:R→Rg:\mathbb{R}\to\mathbb{R} be given as g(x)=2x−3g(x)=2x-3. Then, the sum of all the values of xx for which f−1(x)+g−1(x)=132f^{-1}(x)+g^{-1}(x)=\frac{13}{2} is equal to.
  1. (1)22
  2. (2)55Official answer
  3. (3)33
  4. (4)77

Official answer

Option 2

NTA final key.

Chapter
Relations and Functions
Topic
Functions and Domain
Idea tested
Domain and Range of Inverse Functions

Same idea in other shifts

Asked 3× in all
  1. 4 Apr 2026, Shift 2 · Q1For the function f:[1,∞)→[1,∞)f:[1,\infty)\to[1,\infty) defined by f(x)=(x−1)4+1f(x)=(x-1)^4+1, among the two statements: (I) The set…HardOther
  2. 17 Mar 2021, Shift 1 · Q69The inverse of y=5log⁡xy=5^{\log x} is :EasySingle correct

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.