Question

How do you find the domain of `f(x) = sqrt (x^2 - 2x + 5)`?

Answer 1

The domain of this function is the `RR` set or, in interval notation, `(-oo, oo)`.

This is because the condition that applies here is `x^2-2x+5>=0`.

The graph of the function `x^2-2x+5` shows us that this expression takes positive values for all x. Therefore, we have no restriction for our choice of x values, which can be any real number.

graph{x^2-2x+5 [-10.67, 9.33, -0.68, 9.32]}