Question

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

Answer 1

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}`.