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

↳Redirected from "Suppose that I don't have a formula for #g(x)# but I know that #g(1) = 3# and #g'(x) = sqrt(x^2+15)# for all x. How do I use a linear approximation to estimate #g(0.9)# and #g(1.1)#?"
1 Answer
Bill K.
Feb 16, 2016

The domain is the set of all real numbers #RR# and the range is the interval #[2,infty)#.

Explanation:

You can plug in any real number you want into #f(x)=x^2+2#, making the domain #RR=(-infty,infty)#.

For any real number #x#, we have #f(x)=x^2+2\geq 2#. Furthermore, given any real number #y\geq 2#, picking #x=pm sqrt(y-2)# gives #f(x)=y#. These two facts imply that the range is #[2,infty)={y \in RR : y \geq 2}#.

Related questions
See all questions in Domain and Range of a Function
Impact of this question
1626 views around the world
You can reuse this answer
Creative Commons License