What is the domain for p(x) = x^2 - 2x + 9p(x)=x2−2x+9?

1 Answer
Grégory V.
Jul 6, 2015

p(x)p(x) is defined AAx in RR (=for all real numbers)

Explanation:

The domain of definition (or simply the domain) of a function is the set of "input" or argument values for which the function is defined.

(Source : Domain of a function, Wikipedia)

Your function p(x) is composed by 3 terms. The domain of p(x) is the intersection of each domain of each term.

Therefore : Domain of p(x) :
"Domain of x^2" nn "domain of -2x" nn "domain of 9"

Domain of 9 : No problem, it's well defined for every value of x
Domain of 9 : RR

Domain of -2x : No problem again, it's defined for every value of x
Domain of -2x : RR

Domain of x^2 : Same thing, x^2 can be calculate for every value of x, no forbidden value here.
Domain of x^2 : RR

To conclude :

Domain of p(x) : RR nn RR nn RR = RR


Note : If you have to answer to this question in an exercise, you can conclude with one argument :

"Each term of the function is defined on RR that's why the function is defined on RR too."

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