# Absolute Value Function

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Definition: - The absolute value function or function of modulus of a real number x is denoted by | x | and

is defined as follows:

F (x) = | x | = x            when x > 0

F (x) = | x | = 0           when x = 0

F (x) = | x | = - x         when x < 0

We know that for any real number x, either x > 0 or, x = 0 or, x < 0.

Therefore, from the definition of | x | given as above, it readily follows that the value of | x | can never be

negative.

For example: - If x = 3 then | x | = | 3 | = 3           [since | x | = x when x> 0]

If x = - 3 then | x | = | - 3 | = - (- 3) = 3                    [since | x | = - x when x < 0]

Question 1: - Find the value of the function

F (x) = | x – 1|            at x = 0 and x = 2.

Solution: - f (x) = | x – 1|

At x = 0           f (0) = | 0 – 1| = | - 1| = 1

At x = 2           f ( 2) = | 2 – 1| = | 1 | = 1

Question 2: - If f (x) = | 2 x – 5 |, find the value of the function at x = 2.

Solution: -When x = 2        then f (2) =| 2 (2) – 5 | = |4-5| =|-1|=1