Question 124448: State the domain of the following:
h(x)=3x^2+5x-3
m(x)=3/x^2+7
Any suggestions?
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! For a more complete explanation of domain and range, please see my website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Look for the "MATH IN LIVING COLOR" link on my homepage, choose "College Algebra", and look for Section 2.07 "Functions, Domain, and Range." On this page, you will find a special explanation and examples solved in "LIVING COLOR." This is one of my latest explanations. It may be helpful to anyone who has trouble with the traditional explanations of Domain and Range!!
Domain is the set of all possible x values. To find the domain, look at restrictions that may apply! At most levels of math, there are only TWO restrictions to worry about.
First, if there are denominators, then you must be careful that denominators are NOT allowed to equal zero.
Second, if there are square roots (or 4th roots, 6th roots, etc.), then radicands (that is, what is inside the radical!) cannot be negative. In other words, radicands must be greater than or equal to zero!!
Now, for your two problems: 
There are NO denominators and NO radicals, so therefore, there are NO restrictions. If there are no restrictions, then ANY value of x is allowed, so the domain is all real values.
There is a denominator in this problem, so the denominator  must NOT equal zero. So the domain is all values of x except the value of 0.
Check out my webpage for additional explanation!!
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