anonymous
  • anonymous
Find the domain of the function f(x)= x^2/(7x-1) and leave your answer in set notation.
Mathematics
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
\[f(x)=\frac{ x ^{2} }{ 7x-1 }\]
perl
  • perl
The domain is the set of all real number inputs that make sense. Does it make sense to divide by zero?
imqwerty
  • imqwerty
R-{1/7}

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theEric
  • theEric
I agree with @perl. The thing is, ALL functions have domains - that is a required for a function to be a function. Just, it's \(\it{assumed}\) a lot of the time. So, when no one tells you what it is, you have to assume that your \(x\) can be any value that gives you a result in the "range." That is the range part of the domain and range that are needed for the function. Normally, we make another assumption - the range is real numbers only (no \(\sqrt{-1}\), for sure). So, the result of the function needs a value! Some expressions are undefined, like \(\dfrac{\text{anything}}0\). So, if some value would make \(f(x)\) be \(\dfrac{\text{anything}}0\), then \(x\) is NOT that. In other problems, you might see something like \(g(x)=\sqrt x\). If \(x\) is negative, like \(\sqrt{-4}\), the result is not real, and we don't want it. There, we say \(x\) is NOT negative, so \(x>0\).

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