Classification of Functions

If a set $A$ has $m$ elements and the set $B$ has $n$ elements, then the number of injections from $A$ to $B$ is

Let $f=\left\{\right(2,7),(3,4),(7,9),(-1,6),(0,2),(5,3\left)\right\}$ be a function from  $A=\{-1,0,2,3,5,7\}$ to $B=\{2,3,4,6,7,9\}$,find wether it is one-one and onto function or not

If a set $A$ has $m$ elements and set $B$ has $n$ elements and the number of injections from $A$ to $B$ is $2520.$ Then $m$ is equal 

Let $A$ be the set of all $3\times 3$ scalar matrices with real entries. If $f:A\to R$ is defined by, then $f\left(m\right)=det\left(m\right) \forall m\in A,$ then $\text{'}f\text{'}$ is ______

The function $f:R\to R,$ is given by $f\left(x\right)=\frac{x}{1+\left|x\right|}$, is

Let $f:R\to R$ be a function defined by $f\left(x\right)=\frac{e^{\left|x\right|}-e^{-x}}{e^x+e^{-x}}$, then $f$ is

$f: R\to R, f\left(x\right)=\frac{\sin \left(\pi \left\{x\right\}\right)}{x^4+3x^2+7}$ where $\{*\}$ is a fractional function, then

The function f : [0, 3] → [1, 29], defined by f(x) = 2x³ - 15x² + 36x + 1, is

If $f: R\to S$, defined by $f\left(x\right)=\mathrm{sin }x-\sqrt{3}\mathrm{ cos }x+1$, is onto, then the interval $S$ is

The function $f :R\to \left[-\frac{1}{2},\frac{1}{2}\right]$ defined as $f\left(x\right)=\frac{x}{1+x^2},$ is:

$f: R\to R, f\left(x\right)=\frac{\sin \left(\pi \left\{x\right\}\right)}{x^4+3x^2+7}$ where $\{*\}$ is a fractional function, then

$f:R\to R,f\left(x\right)=x^2+3x+4$ is--

The function $f:R\to R$, defined by $f\left(x\right)=2x+\left|\cos x\right|$ is

Let $\mathrm{F}$ denotes the set of all onto functions from $\mathrm{A}=\left\{a_1,a_2,a_3,a_4\right\}$ to $B=\left\{x,y,z\right\}$. A function $f$ is chosen at random from $\mathrm{F}.$ The probability that $f^{–1}\left(\mathrm{t}\right)$ consists of exactly one element is

Let $R$ be the set of all real numbers and $f:R\to R$ be a continuous function. Suppose $\left|f\right(x)-f(y\left)\right|\ge |x-y|$ for all real numbers $x$ and $y.$ Then

Let $f:\left[0,1\right]\to R$ be an injective continuous function that satisifes the condition $-1<f\left(0\right)<f\left(1\right)<1$ Then, the number of functions $g:\left[-1,1\right]\to \left[0,1\right]$ such that $\left(gof\right)\left(x\right)=x$ for all $x\in \left[0,1\right]$ is

Let $f:\left[0,1\right]\to \left[-1,1\right]$ and $g:\left[-1,1\right]\to \left[0,2\right]$ be two functions such that $g$ is injective and $gof:\left[0,1\right]\to \left[0,2\right]$ is surjective. Then,