Codomain

Q. If a function is defined from $A$ to $B$ as


then the total number of elements in co-domain of function is

Q. If a function is defined from $A$ to $B$ as


then the total number of elements in domain of function is

Q. The function $f:A\to B$ defined by $f\left(x\right)=-x^2+6x-8$ is a bijection if

1. $A=[-3,\infty )\text{and}B=[1,\infty )$
2. $A=[3,\infty )\text{and}B=(-\infty ,1]$
3. $A=(-\infty ,3]\text{and}B=(-\infty ,1]$
4. $A=(-\infty ,-3]\text{and}B=(-\infty ,-1]$

Q. Let $f\left(x\right)$ and $g\left(x\right)$ be bijective functions where $f:\{a,b,c,d\}\to \{1,2,3,4\}$ and $g:\{3,4,5,6\}\to$ $\{w,x,y,z\},$ respectively. Then, the number of elements in the range set of $g\left(f\right(x\left)\right)$ is

Q. Domain of the function $f\left(x\right)=\sqrt{\left[x\right]-x}+\frac{1}{\sqrt{25-x^2}}$ contains the following subset(s), where $[.]$ represents greatest integer function

1. $\{-3,0,3\}$
2. $\{-4,-2,1\}$
3. $\{-2,3,5\}$
4. $\{0,2,4\}$

Q. If a function $f:\{1,2,3,4\}\to \{1,2,3,4,5,6,7,8,9\}$ is defined, then the function $f$ can be

1. $f\left(x\right)=2x+1$
2. $f\left(x\right)=|x|$
3. $f\left(x\right)=x^2$
4. $f\left(x\right)=x-1$