SOLUTION: what is the domain of the function f(x)=3x^2/x^2-49

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Question 867044: what is the domain of the function f(x)=3x^2/x^2-49
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
You cannot divide by zero. So x%5E2+-+49 cannot be zero.


If it were, then


x%5E2+-+49+=+0


%28x-7%29%28x%2B7%29+=+0


x-7=0 or x%2B7+=+0


x=7 or x=-7


These two values cause the denominator to be zero.


So they must be kicked out of the domain to make sure the entire rational expression is defined.


Therefore, the domain is the set of all real numbers BUT x cannot equal -7 and x cannot equal 7. The value of x can be any other number.


In interval notation, the domain is \left(-\infty,-7\right)\cup\left(-7,7\right)\cup\left(7,\infty\right)