Goodmarks

Mathematics · JEE

Important Questions: The composition of functions for JEE

5+ syllabus-aligned questions available

Quick answer

The most important The composition of functions questions for JEE cover conceptual traps, standard results, and numerical patterns from The composition of functions. Goodmarks provides 5+ high-yield MCQs with full solutions.

Focus on what matters most. These important The composition of functions questions cover high-weightage concepts from The composition of functions — the topics JEE repeats every year.

Syllabus context

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

Free sample questions

Attempt 5 free MCQs for The composition of functions. Unlock the full bank with Pro.

Unlock full bank
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} ?
Q5MathsUnit 1: Sets, Relations and Functions
If f:R→R\boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} is defined by f(x)=2x−\boldsymbol{f}(\boldsymbol{x})=\boldsymbol{2} \boldsymbol{x}- 2, then (f∘f)(x)+2=(f \circ f)(x)+2=

Want unlimited The composition of functions practice?

Pro unlocks the full question bank, topic filters, and attempt history.

Get started freeView Pro plans

Popular questions in The composition of functions

Frequently asked questions

What makes a The composition of functions question "important" for JEE?

Important questions test core concepts that appear frequently across JEE Main and Advanced papers — definitions, standard formulas, and classic problem types.

Which subtopics in Sets, Relations and Functions are high-weightage?

Key areas include The composition of functions. Prioritise these before moving to edge cases.

How many important questions should I revise?

Revise 30–50 important MCQs per unit in the last month before JEE. Focus on questions you got wrong at least once.

Can I practise only important questions on Goodmarks?

Pro users can filter by unit and subtopic to target high-yield areas. Free users can attempt sample questions on this page.

Related topics