Embibe Experts Solutions for Chapter: Functions, Exercise 1: WBJEE 2020

Let $f\left(x\right)=\sqrt{x^2-3x+2}$ and $g\left(x\right)=\sqrt{x}$ be two given functions. If $S$ be the domain of $fog$ and $T$ be the domain of $gof$, then

If $f:S\to R,$ where $S$ is the set of all non-singular matrices of order $2$ over $R$ and $f\left[\left(\begin{array}{ll}a& b\\ c& d\end{array}\right)\right]=ad-bc,$ then

Let $A=\left\{x\in R:-1\le x\le 1\right\}$ and $f:A\to A$ be a mapping defined by $f\left(x\right)=x\left|x\right|$. Then $f$ is

Let $S, T, U$ be three non-void sets and $f:S\to T, g:T\to U$ be so that $gof:S\to U$ is surjective. Then,

The value of $\underset{x\to 0^{+}}{\lim }\frac{x}{p}\left[\frac{q}{x}\right]$ is (where $\left[·\right]$ represents greatest integer function)

Let $f\left(x\right)=\sin x+\cos ax$ be a periodic function. Then,

Let $f:X\to Y$ and $A, B$ are non-void subsets of $Y,$ then (where the symbols have their usual interpretation)

Consider the function $y={\log }_a\left(x+\sqrt{x^2+1}\right)$ $a>0,a\ne 1$. The inverse of the function