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The composition of functions Concepts for JEE

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Quick answer

Master The composition of functions by understanding definitions, standard results, and typical JEE question patterns — then practise with syllabus-aligned MCQs on Goodmarks.

Build clear conceptual foundations for The composition of functions before speed practice. This guide covers what JEE expects and how to test yourself with MCQs.

Concept explainer

The composition of functions is a core JEE Main Mathematics subtopic under Sets, Relations and Functions. Master the definitions, standard results, and typical MCQ patterns tested in JEE Main and Advanced.

Key points

  • Understand the definition and scope of The composition of functions in the JEE syllabus
  • Memorise key formulas and standard results linked to The composition of functions
  • Practise 20–40 syllabus-aligned MCQs with step-by-step solutions

JEE tips

  • Revise The composition of functions with a one-page formula sheet before attempting mixed tests
  • After each practice set, log mistakes specific to The composition of functions and reattempt after 48 hours

Common trap

Students often rush The composition of functions questions without checking units, sign conventions, or boundary conditions — always verify assumptions before calculating.

Syllabus context

Part of Sets, Relations and Functions in JEE Main Mathematics.

Free sample questions

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Q1MathsUnit 1: Sets, Relations and Functions
Let f(x)=2100x+1\boldsymbol{f}(\boldsymbol{x})=\mathbf{2}^{100} \boldsymbol{x}+\mathbf{1} g(x)=3100x+1\boldsymbol{g}(\boldsymbol{x})=\boldsymbol{3}^{100} \boldsymbol{x}+\mathbf{1} Then the set of real numbers x such that f(g(x))=x\boldsymbol{f}(\boldsymbol{g}(\boldsymbol{x}))=\boldsymbol{x} is
Q2MathsUnit 1: Sets, Relations and Functions
Assertion Let ff and gg be increasing and decreasing functions respectively from [0,∞][0, \infty] to [0,∞].Let⁡h(x)=f(g(x)).[0, \infty] . \operatorname{Let} h(x)=f(g(x)) . If h(0)=0,h(0)=0, then h(x)h(x) is always zero Reason h(x)h(x) is an increasing function of xx
Q3MathsUnit 1: Sets, Relations and Functions
If f:R→R\boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} and g:R→R\boldsymbol{g}: \boldsymbol{R} \rightarrow \boldsymbol{R} are defined by f(x)=x−[x]\boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}-[\boldsymbol{x}] and g(x)=[x]\boldsymbol{g}(\boldsymbol{x})=[\boldsymbol{x}] for x∈R,\boldsymbol{x} \in \boldsymbol{R}, where [x][\boldsymbol{x}] is the greatest integer not exceeding x,x, then for every x∈x \in R,f(g(x))=\boldsymbol{R}, \boldsymbol{f}(\boldsymbol{g}(\boldsymbol{x}))=
Q4MathsUnit 1: Sets, Relations and Functions
Read the following information and answer the three items that follow: Let f(x)=x2+2x−5\boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}+\boldsymbol{2} \boldsymbol{x}-\boldsymbol{5} and g(x)=\boldsymbol{g}(\boldsymbol{x})= 5x+305 x+30 What are the roots of the equation g[f(x)]=0?\boldsymbol{g}[\boldsymbol{f}(\boldsymbol{x})]=\mathbf{0} ?

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