Amit M Agarwal Solutions for Chapter: Fundamentals of Relation and Function, Exercise 4: Entrances Gallery

The range of the function $f\left(x\right)={\log }_e\left(3x^2+4\right)$ is equal to

Let, $R$ be the set of real numbers and the functions $f:R\to R$ and $g:R\to R$ be defined by $f\left(x\right)=x^2+2x-3$ and $g\left(x\right)=x+1$. Then, the value of $x$ for which $g\left(f\left(x\right)\right)=f\left(g\left(x\right)\right)$ is

Let, $A=\left\{x,y,z\right\}$ and $B=\left\{a,b,c,d\right\}$. Which one of the following is not a relation from $A$ to $B$?

If $f\left(x\right)=3-x,-4\le x\le 4$, then the domain of ${\log }_e\left(f\left(x\right)\right)$ is

Let, $f=\left\{\left(0,-1\right),\left(-1,-3\right),\left(2,3\right),\left(3,5\right)\right\}$ be a function from $Z$ to $Z$, defined by $f\left(x\right)=ax+b$. Then

If $f\left(x\right)=x^2-1$ and $g\left(x\right)={\left(x+1\right)}^2$, then $\left(gof\right)\left(x\right)$ is

Let, $R$ be the set of real numbers and the mapping $f:R\to R$ and $g:R\to R$, be defined by $f\left(x\right)=5-x^2$ and $g\left(x\right)=3x-4$, then the value of $\left(fog\right)\left(-1\right)$ is

Let, $A=\left\{-1,0,1,2\right\}, B=\left\{4,2,0,-2\right\}$ and $f:A\to B \& g:A\to B$, be functions defined by $f\left(x\right)=x^2-x$ and $g\left(x\right)=2\left|x-\frac{1}{2}\right|-1$. Then