Question 173901
The domain of a function is the set of values for which the function is defined.  Since {{{x^2-2x+7}}} produces a real number for any real number value of {{{x}}}, in other words, {{{p(x)}}} is real for all real {{{x}}}, the domain is the set of all real numbers.


Contrast this with {{{f(x)=1/(x-1)}}}.  Since the value 1 would make the denominator be zero, {{{f(x)}}} is not defined at {{{x=1}}}, so the domain here is all real numbers such that {{{x<>1}}}.


Consider  {{{g(x)=sqrt(x)}}}.  {{{sqrt(x)}}} is not defined in the reals for any value of x that is negative, so the domain of {{{g(x)}}} is the set of all real numbers such that {{{x>=0}}}.


See?


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