Not sure on his format, I have to figure out which mapping is not linear

Question

We have L:$C^0 \to \mathbb{R}$, $L(f) = f\left(\frac12\right)$. He wants to know if this is linear.

Is his formatting indicating no matter who I pick for $L(x)$ it will equal $\frac12$? IF I pick L(5) = 1/2 always

Answer 1

$f$ is a function from $C^0$.

$L$ is a mapping that maps $f$ to a real value, that particular value is chosen to be $f(0.5)$.

Answer 2

Note that we have for $f,g$ continuous functions, $a,b$ constants $$ L(af+bg)=(af+bg)(1/2)=af(1/2)+bg(1/2) $$ by the way we understand summing two functions $f$ and $g$.