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

May 21, 2015

The domain of this function is the $\mathbb{R}$ set or, in interval notation, $\left(- \infty , \infty\right)$.

This is because the condition that applies here is ${x}^{2} - 2 x + 5 \ge 0$.

The graph of the function ${x}^{2} - 2 x + 5$ 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]}