Match the following 

	List - I		List - II
I)	$f:R\to R$ defined by $f\left(x\right)=ax+b$ is	P)	Injection but not surjection
II)	$f:R\to R$ defined by $f\left(x\right)=\left[x\right]$ is	Q)	Surjection but not Injection
III)	$f:R\to \left[0,\infty \right)$ defined by $f\left(x\right)=\left|x\right|$ is	R)	Bijection
IV)	$f:N\to N$ defined by $f\left(x\right)=x^3$ is	S)	Neither Injection nor Surjection

I) $f\left(x_1\right)=f\left(x_2\right)$

$a{x}_1+b=a{x}_2+b$

$x_1=x_2$

$\Rightarrow f$ is one-one $y=ax+b$

$x=\frac{y-b}{a}\Rightarrow f$ is onto

$\therefore f$ is a bijection

II) Different elements has same image.

Range is not equal to co-domain of f  is neither injection nor surjection

III) Different elements have same image.

Surjection but not injection

IV)  Different elements have same image

Range is not equal to co-domain.