The range of the function $f\left(x\right)=\left|x\right|$ is

Important Questions on Fundamentals of Relation and Function

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 2 - Fundamentals of Relation and Function>Target Exercises>Q 21

If $f$ and $g$ are two functions defined as  $f\left(x\right)=x+2,x\le 0;g\left(x\right)=3,x\ge 0$, then the domain of $f+g$ is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 2 - Fundamentals of Relation and Function>Target Exercises>Q 22

If ${\left[x\right]}^2-5\left[x\right]+6=0$, where $\left[·\right]$, denotes the greatest integer function, then

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 2 - Fundamentals of Relation and Function>Target Exercises>Q 23

If $f\left(x\right)=1-\frac{1}{x}$, then $f\left\{f\left(\frac{1}{x}\right)\right\}$ is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 2 - Fundamentals of Relation and Function>Target Exercises>Q 24

Let, $f\left(x\right)=\frac{x-1}{x+1}$, then $f\left\{f\left(x\right)\right\}$ is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 2 - Fundamentals of Relation and Function>Target Exercises>Q 25

Two functions $f$ and $g$ are said to commute, if $\left(fog\right)\left(x\right)=\left(gof\right)\left(x\right),\forall x$, then which one of the following functions are commute?

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 2 - Fundamentals of Relation and Function>Target Exercises>Q 26

If $f\left(x\right)=x^2+1$, then the value of $\left(fof\right)\left(x\right)$ is equal to

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 2 - Fundamentals of Relation and Function>Target Exercises>Q 27

If $f\left(x\right)$ is defined on $\left[0,1\right]$ by the rule $f\left(x\right)=\left\{\begin{array}{cl}x,& \mathrm{if} x\in Q\\ 1-x,& \mathrm{if} x\notin Q\end{array}\right.$, then for $x\in \left[0,1\right]$

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 2 - Fundamentals of Relation and Function>Target Exercises>Q 28

If $f\left(x\right)=\left\{\begin{array}{ll}{x}^3+1,& x<0\\ x^2+1,& x\ge 0\end{array}, g\left(x\right)=\left\{\begin{array}{ll}{\left(x-1\right)}^{1/3},& x<1\\ {\left(x-1\right)}^{1/2},& x\ge 1\end{array}\right.\right.$, then $\left(gof\right)\left(x\right)$ is equal to