Question

Find the domain of the real valued function: f(x) = $\sqrt{x^{2} - 25}$

Answer 1

The $\textbf{domain}$ of function $\textbf{f(x)}$ is the set of all values for which function is defined.

we have to find domain of real valued function : f(x) = $\sqrt{x^2-25}$

To define f(x),

x² - 25 ≥ 0 [ because we know, square root is possible only of positive terms ]

or, (x - 5)(x + 5) ≥ 0

x ≥ 5 or, x ≤ -5

hence, domain of function $\in (-\infty,-5]\cup[5,\infty)$