Question

Match the following lists :

1) $f:R\to R$ defind by $f\left(x\right)=ax+b$ is $(a\ne 0)$	a) injection but not surjection
2) $f:R\to R$ defind by $f\left(x\right)=\left[x\right]$ is	b) surjection but not injection
3) $f:R\to [0,\infty )$ defind by $f\left(x\right)=\left|x\right|$ is	c) bijection
4) $f:N\to N$ defind by $f\left(x\right)=x^3$ is	d) neither injection nor surjection

• A. $1-c,2-d,3-a,4-b$
• B. $1-c,2-d,3-b,4-a$
• C. $1-d,2-c,3-b,4-a$
• D. $1-d,2-c,3-a,4-b$

Answer 1

The correct option is B $1-c,2-d,3-b,4-a$

(I) $f\left(x\right)=ax+b,a\ne 0$
$f\left(x\right)$ will be increasing or decreasing depending on a.
So it is one-one & onto.
(II) $f\left(x\right)=\left[x\right]$
neither one-one nor onto
(III) $f\left(x\right)-\mid x\mid$
onto but not one-one
(IV) $f\left(x\right)=x^3$
one-one but not onto.