Question 466439: any help with this would be great. find the domain of the function. g(x) = 5/2-9x
Found 2 solutions by Scorinitron, tinbar:
Answer by Scorinitron(19)   (Show Source):
You can put this solution on YOUR website! g(x)=(5)/(2)-9x
The domain of the rational expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Answer: All real numbers
Answer by tinbar(133)  (Show Source):
You can put this solution on YOUR website! A domain of a function is just a set of values that are "acceptable" to the function.
g(x) = 5/2-9x. The function depends on the value x, so to figure out it's domain, we need to figure out all the numbers that make sense when they are substituted for x in the function.
in g(x) x only shows up once, namely the 9x term. This term asks us to take x and multiply it by 9, so are there any numbers that we cannot multiply by 9? No! Obviously not! We can always multiply a number by 9. Then next, after we multiply x by 9 we must subtract it from 5/2. Is there a number that we cannot subtract from 5/2? Once again, no, every number can be subtracted by 5/2.
The set of numbers that contain the ones that are valid for this function, like positive numbers, negative numbers, rational numbers, irrational numbers, 0 are in a set called the Real numbers. So the answer to this question is g(x) has domain of all values x, such that x belong to the set of Real numbers.
Now you might wonder, what kind of function has a more restricted domain. It seems like all addition, subtraction, multiplication and division can be performed on any number, so therefore you might ask, shouldn't all functions have this same domain of Real numbers?
Consider f(x)=1/x
This has a more restricted domain. For the most part we can take any number and divide 1 by that number. But is this entirely true for all numbers? Consider this statement, it will be obvious by my point will be illustrated, 6/3=2, you already know this to be true, however, what might not be so obvious is the complementing relationship that 6/3=2 IF and ONLY IF 3*2=6, so basically if 3*2 did not equal 6, then 6/3 could not equal 2. So back to our function, we will find we cannot divide 1 by 0, since if there were a valid number for 1/0, let's call it m, then like in the example of 6/3=2, we would require that m*0=1, but we know for any number, 0 times that number is 0!
So what does all that mean for f(x)? Well it basically means that ALMOST all numbers are valid for the function's domain, but we found 0 cannot work since it defies Math! So f(x) is an example of a function with a more restricted domain, namely it's domain is the set of values x, such that x is in the Real numbers set AND that x is not 0 (this is all a fancy way of just saying all the numbers but 0)
Try finding the domain for h(x)=1/(x-5). Basically you want to ask yourself whether you can find a number that doesn't make sense for the function.
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