SOLUTION: find (f-g)(x). What is the domain of f/g f(x)=2x-5 g(x)=2-x

Algebra ->  Graphs -> SOLUTION: find (f-g)(x). What is the domain of f/g f(x)=2x-5 g(x)=2-x      Log On


   

Question 147184: find (f-g)(x). What is the domain of f/g
f(x)=2x-5 g(x)=2-x
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given property


Plug in f%28x%29=2x-5 and g%28x%29=2-x


f%28x%29-g%28x%29=2x-5-2%2Bx Distribute.


f%28x%29-g%28x%29=3x-7 Combine like terms








Start with the given property


Plug in f%28x%29=2x-5 and g%28x%29=2-x


2-x=0 Set the denominator equal to zero. Remember, dividing by 0 is undefined. So if we find values of x that make the denominator zero, then we must exclude them from the domain.



-x=0-2Subtract 2 from both sides


-x=-2 Combine like terms on the right side


x=%28-2%29%2F%28-1%29 Divide both sides by -1 to isolate x



x=2 Divide





Since x=2 makes the denominator equal to zero, this means we must exclude x=2 from our domain

So our domain is:

which in plain English reads: x is the set of all real numbers except x%3C%3E2

So our domain looks like this in interval notation


note: remember, the parenthesis excludes 2 from the domain

If we wanted to graph the domain on a number line, we would get:

Graph of the domain in blue and the excluded value represented by open circle

Notice we have a continuous line until we get to the hole at x=2 (which is represented by the open circle).
This graphically represents our domain in which x can be any number except x cannot equal 2