SOLUTION: f(x) = 2x-|2x-3| Rewrite as a piecewise-defined function, graph, determine domain of f, range of f, intervals over which f is increasing, decreasing, constant (if any). Write u

Algebra ->  Absolute-value -> SOLUTION: f(x) = 2x-|2x-3| Rewrite as a piecewise-defined function, graph, determine domain of f, range of f, intervals over which f is increasing, decreasing, constant (if any). Write u      Log On


   

Question 846158: f(x) = 2x-|2x-3|
Rewrite as a piecewise-defined function, graph, determine domain of f, range of f, intervals over which f is increasing, decreasing, constant (if any). Write using interval notation.
I have x=3/4 and x=no solutions. Can you please help. Thanks
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
When 2x-3%3E0,2x%3E3, x%3E3%2F2 then
f%28x%29=2x-2x%2B3
f%28x%29=3
When 2x-3%3C0, x%3C3%2F2 then
f%28x%29=2x%2B2x-3
f%28x%29=4x-3
graph%28300%2C300%2C-5%2C5%2C-5%2C5%2C2x-abs%282x-3%29%29
So then f%28x%29=4x-3for (-infinity,3%2F2) and f%28x%29=3 for (3%2F2,infinity)