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Answer:
option a
Explanation:
f(x) = |x-4| indicates that f(x) is always positive
When x ≥ 4, (x - 4) is positive
When x < 4, (x - 4) is negative
⇒ -(x - 4) is positive
⇒ -x + 4 is positive
Therefore option (a) is correct
The piecewise function representation of f(x) = |x - 4 can be written as follows:
f(x) =
x - 4, for x > 4
-x + 4, for x < 4
√(x - 4), for x ≥ 0
-1/2(x - 4), for x < 0
This representation breaks down the function into different cases based on the value of x, allowing for different expressions to be used in different intervals.
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