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Important Questions: The composition of functions for JEE

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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
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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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.

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

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

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