Types of Functions

Define into function and write one example.

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

A bijective function is both one-one and onto.

The function $f:N\to N$ given by $f\left(x\right)=2x$ is

 Let $A=\left\{x:-\frac{\pi }{2}\le x\le \frac{\pi }{2}\right\}$ and $B=\{x:-1\le x\le 1\}$. If $f:A\to B$ is defined by $f\left(x\right)=\sin x$, then $f\left(x\right)$ is

If $f:R\to \left[-\mathrm{1,1}\right]$ be a function defined as $f\left(x\right)=\text{sin}\left(\frac{x^2-8}{x^2+2}\right)\text{,}$ then $f$ is

Let a function $f$ such that $f\left(x\right)=\frac{2x}{x-1}$ defined in the interval $f:(-\infty ,0]\to R$, then $f$ is:

Let  $f\text{ : }\text{R}\to \text{R}$ be defined by $f\left(x\right)=\frac{\left|x\right|-1}{\left|x\right|+1}$ then for the function $f$,tick the appropriate option.

A mapping $f:N\to N$, where $N$ is the set of natural numbers is defined as

$f\left(n\right)=\left\{\begin{array}{c}{n}^2, \mathrm{for} n \mathrm{odd}\\ 2n+1, \mathrm{for} n \mathrm{even}\end{array}\right.$

For $n\in N$. Then, comment on $f$, whether it is one-one/many-one and into/onto :

If the function $f\left(x\right)=x^2+bx+3, x\in \left[0,1\right]$ is not injective, then complete set of values of $b$will be

Let $f:R\to \left(0,\frac{\pi }{2}\right]$ defined by $f\left(x\right)={\csc }^{-1}\left(a{x}^2-2px+4\right)$ where $a,p\in N$ is surjective then find smallest value of $2(a+p)$

Let $f:R\to [-1, 1]$ defined by $f\left(x\right)=\frac{x^2-1}{x^2+1}$, then which of the following is/are INCORRECT?

Let $f:R\to \left[0,1\right]$ be a function defined by $f\left(x\right)=\min \left\{e^{-x},\left|x^2-1\right|\right\}$. Identify which of the following statement(s) is/are correct?

Let $A=\left\{x:x\in R^{-}\right\}, f:A\to R$ is defined as $f\left(x\right)=\frac{2x}{x-1}$ then $f\left(x\right)$ 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 $f^{–1}$ consists of exactly one element is

Let $f :R\to R$ be defined by $f\left(x\right)=x^4$$,$ then

Function $f :N\to N, f\left(x\right)=2x+3$ is

Let $f:R\to R$ be a function defined by $f\left(x\right)=\frac{x^2-8}{x^2+2}$ .Then, f is

Let $f : R–\left\{x\right\} ⟶R$ be a function defined by $f\left(x\right)=\frac{x-m}{x-n}$ , where $m \ne n$ . Then-