# Let a function

Question:

Let a function $f:(0, \infty) \rightarrow(0, \infty)$ be defined by $f(x)=\left|1-\frac{1}{x}\right|$. Then $f$ is :

1. (1) not injective but it is surjective

2. (2) injective only

3. (3) neither injective nor surjective

4. (4) $f(x)$ is not a function.

Correct Option: , 4

Solution:

$f:(0, \infty) \rightarrow(0, \infty)$

$f(x)=\left|1-\frac{1}{x}\right|$ is not a function

$\because \quad f(1)=0$ and $1 \in$ domain but $0 \notin$ co-domain

Hence, $f(x)$ is not a function.