Mathematics · JEE

Medium The composition of functions MCQs for JEE

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

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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=

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