Example 2

Find as large a set as you can on which the function

is continuous.

sin x is continuous for all x. ln(x + 1) is continuous whenever x + 1 > 0, that is, x > -1. The numerator sin x ln (x + 1) is thus continuous whenever x > -1. The denominator x² - 4 is continuous for all x but is zero when x = ±2. Therefore f(x) is continuous whenever x > -1 and x ≠ 2.