Q. A function $f$ on $R$ into itself is continuous at a point $a$ in $R$, iff for each $\in > 0$, there exists, $\delta > 0$ such that
A) $\left| f(x) - f(a) \right| < \in \Rightarrow |x - a| < \delta$
B) $\left| f(x) - f(a) \right| > \in \Rightarrow |x - a| > \delta$
C) $|x - a| > \delta\left| f(x) - f(a) \right| > \in$
D) $|x - a| < \delta\left| f(x) - f(a) \right| < \in$
Explanation
(a)
A function $f$ on $R$ into itself is continuous at a point $a$ in $R$, iff for each $\in > 0$ there exist $\delta > 0$, such that
$\left| f(x) - f(a) \right| < \in \ \ \ \Rightarrow \ \ \ \ |x - a| < \delta$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.