Find the Domain and Range of f(x)=|x-1|

Find the Domain and Range of $f(x)=|x-1|$

Question: Find the domain and range of the real valued function: $$ f(x)=|x-1| $$

Solution

The modulus function is defined for every real number.

Hence, the domain is: $$ \mathbb{R} $$

Since modulus values are always non-negative, $$ |x-1|\ge0 $$

Minimum value occurs at $$ x=1 $$

$$ f(1)=|1-1|=0 $$

As $x$ moves away from $1$, the value of $f(x)$ increases without bound.

Hence, the range is: $$ [0,\infty) $$

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