What is the domain and range of # f(x) = x^2 + 5#?

1 Answer
Jun 4, 2017

Consider the function,

#f(x) = x^2 + 5#

The domain is the set of all possible values of #x# for which this function is defined.

For #f(x)# to be real valued, all real values of #x# are consistent with the definition of #f(x)#.

Thus, domain is #R#, the set of real numbers.

The range in this case is also #R# since it is a real valued function.

Another thing that might be added is that the codomain which is the set of values in the range #R# to which elements of the domain are mapped.

Well, for any value of #x#, #f(x)# varies from #5# to infinity.

Thus, codomain, extends from #5# to infinity.