f(x) = (5^x - 3^x)/(4^x - 3^x), x ≠ 0

Question

Discuss the continuity of the following functions.

\(f(x) = \frac{5^x - 3^x}{4^x - 3^x},\,x\neq 0\)

f(x) = (5^x - 3^x)/(4^x - 3^x), x ≠ 0

\(=log\frac{5}{4},\) x = 0; at x = 0.

Answer 1

f(x) = (5^x - 3^x)/(4^x - 3^x)

\(\therefore\) f is discontinuous at x = 0