Embibe Experts Solutions for Chapter: Functions, Exercise 1: CUSAT CAT 2017

The domain of the function $f\left(x\right)={\cot }^{-1}\left(\frac{x}{\sqrt{x^2-\left[x^2\right]}}\right)$, for real $x\in \mathrm{ℝ} ($here $\left[x\right]$ is the largest integer less than $x)$ is

The domain of the function ${\sin }^{-1}\left({\log }_2\frac{x^2}{2}\right)$ is

The domain of the real function $f\left(x\right)=\sqrt{x-\frac{x}{1-x}}$ is

If $f\left(x\right).f\left(\frac{1}{x}\right)=f\left(x\right)+f\left(\frac{1}{x}\right)$ and $f\left(4\right)=65$, then $f\left(6\right)$

The solution of the inequality $1+\left|x-1\right|\ge 0$ is

The function $f\left(x\right)=x^2+bx+c$, where $b$ and $c$ real constants, describes

If the function $f:\mathrm{ℝ}\to \mathrm{ℝ}$ is defined by $f\left(x\right)={\left(x^2+1\right)}^{35} \forall x\in \mathrm{ℝ}$, then $f$ is -

The even function of the following is