Mathematics · JEE

Hard The composition of functions MCQs for JEE

5+ syllabus-aligned questions available

Quick answer

Hard The composition of functions MCQs train multi-concept problem solving — attempt after mastering easy and medium sets (5+ on Goodmarks).

Push your limits with hard The composition of functions MCQs designed for JEE Advanced-level thinking. 5+ questions with detailed solutions.

Syllabus context

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

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

Q1MathsUnit 1: Sets, Relations and Functions

Let

\boldsymbol{f}(\boldsymbol{x})=\mathbf{2}^{100} \boldsymbol{x}+\mathbf{1}

\boldsymbol{g}(\boldsymbol{x})=\boldsymbol{3}^{100} \boldsymbol{x}+\mathbf{1}

Then the set of real numbers x such that

\boldsymbol{f}(\boldsymbol{g}(\boldsymbol{x}))=\boldsymbol{x}

Q2MathsUnit 1: Sets, Relations and Functions

Assertion Let

f

and

g

be increasing and decreasing functions respectively from

[0, \infty]

[0, \infty] . \operatorname{Let} h(x)=f(g(x)) .

h(0)=0,

then

h(x)

is always zero Reason

h(x)

is an increasing function of

x

Q3MathsUnit 1: Sets, Relations and Functions

\boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R}

and

\boldsymbol{g}: \boldsymbol{R} \rightarrow \boldsymbol{R}

are defined by

\boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}-[\boldsymbol{x}]

and

\boldsymbol{g}(\boldsymbol{x})=[\boldsymbol{x}]

for

\boldsymbol{x} \in \boldsymbol{R},

where

[\boldsymbol{x}]

is the greatest integer not exceeding

x,

then for every

x \in

\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

\boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}+\boldsymbol{2} \boldsymbol{x}-\boldsymbol{5}

and

\boldsymbol{g}(\boldsymbol{x})=

5 x+30

What are the roots of the equation

\boldsymbol{g}[\boldsymbol{f}(\boldsymbol{x})]=\mathbf{0} ?

Q5MathsUnit 1: Sets, Relations and Functions

\boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R}

is defined by

\boldsymbol{f}(\boldsymbol{x})=\boldsymbol{2} \boldsymbol{x}-

2, then

(f \circ f)(x)+2=

Want unlimited The composition of functions practice?

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

After 70%+ accuracy on medium MCQs and once core formulas are automatic.