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

1 Answer
Feb 11, 2018

Answer:

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

Explanation:

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):}#