Types of Functions

Let $f:R\to R$ be a continuous and one-one function. Then which of the following is true?

 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

Let $f:R^{+}\to R^{+}$ be a mapping define by $f\left(x\right)=x^3+4.$ Then $f$ is

Let $f\left(x\right):\{\begin{array}{c}\begin{array}{cc}x,& x\text{is}\text{rational}\\ 0,& x\text{is irrational}\end{array}\end{array}$ and $g\left(x\right):\{\begin{array}{c}0, x \text{is irrational}\\ x, x \text{is irrational}\end{array}$

If $f:R\to R$ and $g:R\to R,$ then $\left(f-g\right)$ is

The function $f:X\to Y$ defined by $f\left(x\right)=\cos x,$ where $x\in X,$ is one-one and onto if $X$ and $Y$ are respectively equal to

The function undefined is

The number of functions $f$ from $\left\{1,2,3,.....,20\right\}$ onto $\left\{1,2,3,.....,20\right\}$ such that

$f\left(k\right)$ is a multiple of $3$, whenever $k$ is a multiple of $4$, is:
 

Which of the following is not one-one?

$A=\left\{1, 2, 3, 4\right\}, B\left\{1, 2, 3, 4, 5, 6\right\}$ are two sets, and function $f:A\to B$ is defined by $f\left(x\right)=x+2 \forall x\in A$, then the function $f$ is

Let $A=R–\left\{3\right\}$ and $B=R–\left\{1\right\}$. Consider the function$f: A\to B$ defined by $f\left(x\right)=\left(\frac{x-2}{x-3}\right)$ then

Let $A \& B$ be sets.$f:A\times B\to B\times A$ such that $f\left(a,b\right)=\left(b,a\right)$ is 

In each of the following cases, state whether the functions is one-one, onto or bijective. Justify answer.
$f:R\to R$ defined by $f\left(x\right)=3-4x$

Let, $A=\left\{1,2,3\right\}$, $B=\left\{4,5,6,7\right\}$ and let, $f=\left\{\left(1,4\right),\left(2,5\right),\left(3,6\right)\right\}$ be a function $f:A\to B$, $f$ is