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

1 Answer
Grégory V.
Jul 6, 2015

#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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