Question

Calculus question:
Find all values of a such that f is continuous on (-infinity, +infinity)
f(x)= { x+1 xa

Answer 1

the function is continuous at x = a if \[\lim_{x \rightarrow a} f(x) = f(a)\]the limit must exists, then\[\lim_{x \rightarrow a^{+}} f(x) = \lim_{x \rightarrow a^{-}} f(x)\]\[a^2 = a + 1\]\[a^2 - a - 1 = 0\]\[a = \frac{1 + \sqrt{5}}{2}\]or\[a = \frac{1 - \sqrt{5}}{2}\]