Embibe Experts Solutions for Chapter: Functions, Exercise 1: Exercise 1

For $f$ to be a function, what is the domain of $f,$ if $f\left(x\right)=\frac{1}{\sqrt{\left|x\right|-x}} ?$

If $f\left(x\right)=\frac{\sqrt{x-1}}{x-4}$ defines a function on $R$, then what is its domain ?

Let $f:(1,\infty )\to [1,\infty )$ be defined by $f\left(x\right)=\frac{x+2}{x-1}.$ Then,

Let $\left[x\right]$ denote the greatest integer less than or equal to $x.$ Then, the values of $x\in R$ satisfying the equation ${\left[e^x\right]}^2+\left[e^x+1\right]-3=0$ lie in the interval:

Define $f: R\to R$ by $f\left(x\right)=\max \{x+1, 1-x, 2\}.$ Then $f$ is $\_\_\_$

If $f\left(x\right)$ is an even function, where $f\left(x\right)\ne 0,$ then which one of the following is correct?

What is the period of the function $f\left(x\right)=\sin x ?$

If $f$ is a function defined on $(0,1)$ by $f\left(x\right)=\max \{x-[x],-x-[x\left]\right\}$, then $\left(fofofof\right)\left(x\right)$ is equal to ([.] greatest integer function)