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The composition of functions Revision for JEE

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Revise The composition of functions by covering every subtopic once, drilling formulas, then solving 4+ timed MCQs with full solutions.

Use this The composition of functions revision checklist before mocks and the final exam. Reinforce concepts with 4+ syllabus-aligned MCQs on Goodmarks.

Revision checklist

  1. 1.Core idea: The composition of functions
  2. 2.Relates to other subtopics in Sets, Relations and Functions
  3. 3.Union, intersection, complement, power set
  4. 4.Equivalence relations
  5. 5.Master The composition of functions definitions and standard results
  6. 6.Solve 20 timed MCQs for The composition of functions

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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How should I revise The composition of functions before JEE?

Follow the checklist on this page, revise formulas daily, and attempt mixed MCQs every 2–3 days.

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