SOLUTION: f(x) = |x| and g(x) = x - 1. How many solutions x satisfy f(x) = g(x)?

Algebra ->  College  -> Linear Algebra -> SOLUTION: f(x) = |x| and g(x) = x - 1. How many solutions x satisfy f(x) = g(x)?      Log On


   

Question 301368: f(x) = |x| and g(x) = x - 1. How many solutions x satisfy f(x) = g(x)?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29 can take on values of x when x%3E0 and and -x when x%3C0.
f%28x%29=g%28x%29
Create a new function and find out when it equals zero.
h%28x%29=f%28x%29-g%28x%29=0
When x%3E=0
h%28x%29=x-%28x-1%29
h%28x%29=1
When x%3C0
h%28x%29=-x-%28x-1%29=-2x%2B1
.
.
.
In both cases, h%28x%29 will never equal zero.
No solutions where f(x)=g(x).