#### Answer

The domain of the function $f\left( x \right)={{x}^{2}}+6x-3$ is $f=\left( -\infty,\infty \right)$.

#### Work Step by Step

Consider the given function $f\left( x \right)={{x}^{2}}+6x-3$.
We can see that this function contains neither division nor the square root.
Also, the expression ${{x}^{2}}+6x-3$ represents a real number, for every value of $x$.
Therefore, the domain of the given function is the set of all real numbers.
Therefore, the domain of the function $f\left( x \right)={{x}^{2}}+6x-3$ is $f=\left( -\infty,\infty \right)$.