SOLUTION: find the domain of the function g(x)=4/9-4x

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Question 333879: find the domain of the function g(x)=4/9-4x
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

g%28x%29=%284%29%2F%289-4x%29 Start with the given function


9-4x=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.



-4x=0-9Subtract 9 from both sides


-4x=-9 Combine like terms on the right side


x=%28-9%29%2F%28-4%29 Divide both sides by -4 to isolate x



x=9%2F4 Reduce





Since x=9%2F4 makes the denominator equal to zero, this means we must exclude x=9%2F4 from our domain

So our domain is:

which in plain English reads: x is the set of all real numbers except x CANNOT equal 9%2F4

So our domain looks like this in interval notation


note: remember, the parenthesis excludes 9/4 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=9%2F4 (which is represented by the open circle).
This graphically represents our domain in which x can be any number except x cannot equal 9/4