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Write f(x) = |x - 4 as a piecewise function. f(x) = f(x) = x-4, x>4 -x+4, x < 4 √x-4, x ≥ 0 -X 4, x < 0 © 1(2) - {² [x-4, x ≥ 4 4, a < 4 2-4,220​

Write f(x) = |x - 4 as a piecewise function. f(x) = f(x) = x-4, x>4 -x+4, x &lt-example-1
User Abushawish
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2 Answers

4 votes

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


f(x) = \left \{ {{x-4\;\;\;\;\;\;\;\;x\geq 4} \atop {-x+4\;\;\;\;\;x < 4}} \right.

Therefore option (a) is correct

User An Phan
by
8.1k points
2 votes

Answer:

Explanation:

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.

User Chris Cook
by
7.4k points
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