Find all values of a such that f is continuous on (−∞, ∞): 𝑓(𝑥) = { 𝑥 2 𝑥 ≤ 𝑎 2𝑥 + 1 𝑥 > 𝑎 •

Question

Find all values of a such that f is continuous on (−∞, ∞): 𝑓(𝑥) = { 𝑥 2 𝑥 ≤ 𝑎 2𝑥 + 1 𝑥 > 𝑎 • You must use the requirements for continuity to solve, and make sure you explain why it is continuous everywhere, not just at 𝑥 = 𝑎.

Answer 1

a² = 2a + 1; a = 1 + √2 or a = 1 - √2