SOLUTION: Findind the domain of the rational function f(x)= 49x2-16 _________ 2x-6

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Question 878939: Findind the domain of the rational function
f(x)= 49x2-16
_________
2x-6
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
You cannot divide by zero. If the denominator were zero, then

2x-6 = 0

2x = 6

x = 6/2

x = 3

That means if x = 3, then the denominator 2x-6 would be equal to zero.

So x = 3 causes a division by zero error. That forces us to exclude x = 3 from the domain.

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Domain: the set of all real numbers x but x cannot equal 3

Another way to state the domain

\text{Domain: }\left\{x|x\in\mathbb{R},x \neq 3\right\}

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Domain in interval notation:

\left(-\infty,3\right) \cup \left(3,\infty\right)