Question

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​

Answer 1

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

Answer 2

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.