Question

h:R - R, h(x)=|x-1| is onto fnuction?

Answer 1

Answer:

The function $h(x)=|x-1|$ is not an onto function.

Step-by-step explanation:

A function is onto if every element in the codomain has a preimage in the domain. Here the domain and co domain of the function is the set of all real numbers.

The modulus function takes only non negative values. That means for all negative real numbers, there is no preimage in the domain. For example, if we consider the number -2, there does not exist a number $x\in \mathbb{R}$, such that

$|x-1|=-2$

So, the function $h(x)$ is not onto.