Question

What is the domain of the function f(x) = x^2 + 3x + 5?

Answer 1

We need to have (x^2 - 3x + 2) ≥ 0 

That is the same as (x - 2) * (x - 1) ≥ 0 

This happens when both (x - 2) and (x - 1) ≥ 0, which is when x ≥ 2 and when x ≥ 1, so it happens when x ≥ 2. 

It also happens when they are both ≤ 0, which is when (x - 2) and (x - 1) are both ≤ 0. That happens when x ≤ 2 and when x ≤ 1, in other words, when x ≤ 1 

Therefore the domain is {x is real and either x ≤ 1 or x ≥ 2 <---- Answer 

For x in (1,2) (x-2 is negative) and (x - 1) is positive, so their product is negative.