Answer
True
Work Step by Step
Let us assume that both the functions were continuous. Then the values of $f(x)$ and $g(x)$ at $c$ will be equal to the limits as the both functions approaches at $c$.
However, the limits for both the functions are not equal to the $c$ at any point.This contradicts that $f(c)=g(c)$.
Hence, the given statement is true.
