Answer
The domain of the function $f\left( x \right)=3\sqrt{x+5}+7\sqrt{x-1}$ is $\underline{\left[ 1,\infty \right)}$.
Work Step by Step
The domain is the set of values of $x$ for which the function $f(x)$ can be defined.
We see that $\sqrt{x-1}$ cannot be defined for values of $x<1$, but $\sqrt{x+5}$ is defined for every real value of $x$.
Therefore, the function can be defined for all the real values except $x<1$.
Hence, the domain of the function is $\left[ 1,\infty \right)$.
