Answer the following questions related to continuity and discontinuity of real-valued functions.
a. (i) State the algebraic condition that must be satisfied for a function f to be continuous at a point x=a.
b. (ii) Distinguish between a removable discontinuity, a jump discontinuity and an infinite discontinuity. Give one identifying feature of each type.
c. (iii) Let
f(x)={x2−4,3x−2,x<2,x≥2.
Examine the behaviour of f at x=2. Determine whether f is continuous there. If it is not continuous, classify the type of discontinuity found.