Chapter 13 - Partial Derivatives - 13.2 Limits And Continuity - Exercises Set 13.2 - Page 926: 31

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$f(x, y)=\left\{\begin{array}{ll}-1 & , x<0 \\ 1 & , x \geq 0\end{array} \quad g(x, y)=\left\{\begin{array}{ll}1 & , x<0 \\ -1 & , x \geq 0\end{array}\right.\right.$ Then $(g+f)(x, y)=0, \quad(\text { continuous })$ $(g f)(x, y)=0, \quad(\text { continuous })$ But neither of $\mathrm{f}$ or $\mathrm{g}$ are continuous.