Consider the following for the two (02) items that follow: A...

Given $f(xy) = f(x+y)$ for all real values of $x$ and $y$.

Substituting $y = 0$, we get $f(x \cdot 0) = f(x + 0)$, which simplifies to $f(0) = f(x)$ for all real $x$.

This implies that $f(x)$ is a constant function for all real values of $x$.

Since $f(5) = 10$, the constant value of the function is $10$. Thus, $f(x) = 10$ for all $x \in \mathbb{R}$.

We need to find the value of $f(20) + f(-20)$.

$f(20) = 10$

$f(-20) = 10$

$f(20) + f(-20) = 10 + 10 = 20$

Answer: $20$