Question

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

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

Answer 1

The correct option is B $(-\infty ,3]\cup [4,\infty )$

$f$ is defined for all $x$ for which $x^2-7x+12\ge 0$
$\Rightarrow (x-3)(x-4)\ge 0$
$\Rightarrow x\in (-\infty ,3]\cup [4,\infty )$