Answer
The domain of the function $f\left( x \right)=\sqrt{x-1}\text{ +}\sqrt{x+5}$ is $\left[ 1,\infty \right)$.
Work Step by Step
Consider the function,
$f\left( x \right)=\sqrt{x-1}\text{ +}\sqrt{x+5}$
Since, this function involves the square root and the square root of a negative real number is not defined, the expression written inside the square root sign must be non-negative, that is, $x-1\ge 0$ or $x\ge 1$.
Also, $x+5\ge 0$ or $x\ge -5$.
Therefore, the domain of the function $f\left( x \right)=\sqrt{x-1}\text{ +}\sqrt{x+5}$ is $\left[ 1,\infty \right)$.
