Tamil Nadu Board Solutions for Chapter: Relations and Functions, Exercise 14: Exercise 1.6

Let $n\left(A\right)=m$ and $n\left(B\right)=n$ then the total number of non-empty relations that can be defined from $A$ to $B$ is

If $\left\{\right(a,8),(6,b\left)\right\}$ represents an identity function, then the value of $a$ and $b$ are respectively

Let $A=\{1,2,3,4\}$ and $B=\{4,8,9,10\}.$ A function $f:A\to B$ given by $f=\left\{\right(1,4), (2,8), (3,9), (4,10\left)\right\}$ is a

If $f\left(x\right)=2x^2$ and $g\left(x\right)=\frac{1}{3x},$ then $fog$ is

If $f:A\to B$ is a bijective function and if $n\left(B\right)=7,$ then $n\left(A\right)$ is equal to

Let $f$ and $g$ be two functions given by

$f=\left\{\right(0,1), (2,0), (3,-4), (4,2), (5,7\left)\right\}$ 

$g=\left\{\right(0,2),(1,0),(2,4),(-4,2),(7,0\left)\right\}$ then the range of $f\circ g$ is

Let $f\left(x\right)=\sqrt{1+x^2}$ then

If $g=\left\{\right(1, 1),(2, 3),(3, 5),(4, 7\left)\right\}$ is a function given by $g\left(x\right)=\alpha x+\beta$, then the values of $\alpha$ and $\beta$ are