Question

Discuss the continuity of the function f(x) = {(a^x + b^x + c^x - 3)/x :  x ≠0), (logabc : x = 0) at x = 0.

Answer 1

(i) f(0) = log(abc)

(ii) lim _(x→0) f(x)

= loga + logb + logc = log(abc)

(iii) lim_(x→0) f(x) = log(abc) = f(0)

Thus, f(x) is continuous at x = 0