Multiplying a piecewise function by a constant?

Question

For example if i have f(x) = { 10, x != 0, 5, x = 0} and g(x) = 0

Would f(x)g(x) = {0, x!=0 0, x = 0}

Thanks. (Sorry for the bad formatting it is the first time I am using this site)

Answer 1

Well, if $x\neq0$ then $f(x)g(x)=10\cdot{0}=0$, otherwise $f(0)g(0)=5\cdot{0}=0$, so yes, $f(x)g(x)=0$ for all x. More generally, if $g(x)=c$ is a constant, $f(x)g(x)=10c$ for $x\neq0$ and $f(0)g(0)=5c$.