Question

The domain of the function f : R $\to$ R defined by $f(x) = \sqrt{x^2 - 7x + 12}$ is

• A. $( - \infty , 3) \cap ( 4, \infty)$
• B. $( - \infty , 3) \cup ( 4, \infty)$
• C. (3, 4)
• D. $( \infty , 3) \cap (4, \infty)$

Answer 1

Answer: (B)

$( - \infty , 3) \cup ( 4, \infty)$

Answer 2

$f :R\to R$
$f\left(x\right)=\sqrt{x^{2}-7x+12}$
$x^{2}-7x+12 \ge0$
$\left(x-4\right)\left(x-3\right)\ge0$
$\Rightarrow\, x \in(-\infty, 3 ] \cup[4, \infty)$