1.9 Answer

1.9

1.

$f(x)$ is continuous at $x = a$. Then for $c - f(a) > 0$ and $\vert x - a\vert < \delta$, then we have

$$\vert f(x) - f(a)\vert < c - f(a)$$

Thus, $f(x) < f(a) + c - f(a) = c$．