Answer
The value of $f+g$ is $\left[ -4,3 \right]$.
Work Step by Step
Consider the above graph:
Curve ${{C}_{1}}$ represents the values of the function $f\left( x \right)$ and curve ${{C}_{2}}$ represents the values of the function $g\left( x \right)$.
The domain of a function can be defined as the set of all values of x for which the function is defined.
The domain of the function f is $\left[ -4,3 \right]$ and the domain of the function g is $\left[ -5,5 \right]$.
Now, to find the domain of the function $f+g$ which is the intersection of the domain of the function f and g.
Therefore, the domain of the function $f+g$ is $\left[ -4,3 \right]$ as it is common in the domain of both the function f and g.
Hence, the domain of the function $f+g$ is $\left[ -4,3 \right]$.
