SOLUTION: Write the piecewise formula for the given function. f(x) = |2x-1|

SOLUTION: Write the piecewise formula for the given function. f(x) = |2x-1| - 5

Question 1092119: Write the piecewise formula for the given function.
f(x) = |2x-1| - 5
Answer by Edwin McCravy(20066) (Show Source): You can put this solution on YOUR website!


An expression between absolute value bars is equal
to the expression WITHOUT the absolute bars whenever
the expression is ZERO or POSITIVE.

An expression between absolute value bars is equal
to the OPPOSITE of the expression WITHOUT the absolute 
bars whenever what the expression is NEGATIVE.

Therefore

f(x) = |2x-1| - 5 

means: 



but that is not the simplified version.
We need to simplify the expressions on 
the left and solve the inequalities on 
the right:

Simplifying and solving:

(2x-1)-5    -(2x-1)-5     2x-1<0       2x-1>0   
 2x-1-5      -2x+1-5        2x<1         2x>1
  2x-6        -2x-4          x<1/2        x>1/2

So replacing:



Edwin

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