Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# Find the Domain and Range of the Real Valued Function: (Vi) F ( X ) = | X − 1 | - Mathematics

Find the domain and range of the real valued function:

(vi) $f\left( x \right) = \left| x - 1 \right|$

#### Solution

The given real function is f (x) = |x – 1|.
It is clear that |x – 1| is defined for all real numbers.
Hence, domain of f = R.
Also, for x ∈ R, (x – 1) assumes all real numbers.
Thus, the range of is the set of all non-negative real numbers.
Hence, range of f = [0, ∞) .

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 3 Functions
Exercise 3.3 | Q 3.06 | Page 18