Show that f is continuous on (−[infinity], [infinity]). f(x) = 1 − x2 if x ≤ 1 ln(x) if x > 1 On the interval (−[infinity], 1), f is function; therefore f is continuous on (−[infinity], 1). On the interval (1, [infinity]), f is function; therefore f is continuous on (1, [infinity]). At x = 1, lim x→1− f(x) = lim x→1− = , and lim x→1+ f(x) = lim x→1+ = , so lim x→1 f(x) = . Also, f(1) = . Thus, f is continuous at x = 1. We conclude that f is continuous on (−[infinity], [infinity]).