15. Let $f , g$ be two real valued functions defined on the set of real numbers. Which of the following statements are true? (a) If $f ( x )$ is continuous and $g ( x )$ discontinuous then the function $f ( x ) + g ( x )$ is necessarily discontinuous. (b) If $f ( x )$ is continuous and $g ( x )$ discontinuous then the function $f ( x ) \cdot g ( x )$ is necessarily discontinuous. (c) If the functions $f ( x ) , g ( x )$ are discontinuous at a point $c$ in the domain the function $f ( x ) + g ( x )$ is also discontinuous at $c$. (d) If the functions $f ( x ) , g ( x )$ are discontinuous at a point $c$ in the domain the function $f ( x ) \cdot g ( x )$ is also discontinuous at $c$.
15. Let $f , g$ be two real valued functions defined on the set of real numbers. Which of the following statements are true?\\
(a) If $f ( x )$ is continuous and $g ( x )$ discontinuous then the function $f ( x ) + g ( x )$ is necessarily discontinuous.\\
(b) If $f ( x )$ is continuous and $g ( x )$ discontinuous then the function $f ( x ) \cdot g ( x )$ is necessarily discontinuous.\\
(c) If the functions $f ( x ) , g ( x )$ are discontinuous at a point $c$ in the domain the function $f ( x ) + g ( x )$ is also discontinuous at $c$.\\
(d) If the functions $f ( x ) , g ( x )$ are discontinuous at a point $c$ in the domain the function $f ( x ) \cdot g ( x )$ is also discontinuous at $c$.\\