How do you write $f (x) = | 2 x + 3 |$ $f(x) = |2x+3|$ as a piecewise function?

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Answer 1 · 2018-02-11T16:32:53

Use the definition:
$|f(x)| = {(f(x)", "f(x) >= 0),(-f(x)", "f(x) < 0):}$

Given $f(x) = |2x+3|$

Using the definition:

$f(x) = |2x+3| = {(2x+3", "2x+3 >= 0),(-2x-3", "2x+3 < 0):}$

It is good practice to simplify the inequalities:

$f(x) = {(2x+3", "2x >= -3),(-2x-3", "2x < -3):}$

Finished:

$f(x) = {(2x+3", "x >= -3/2),(-2x-3", "x < -3/2):}$

How do you write f(x) = |2x+3|f(x)=|2x+3|f(x) = |2x+3| as a piecewise function?