Examine the continuity of the function f(x) = {(x+1,x≥1)(x^2+1, x<1)

Question

Examine the continuity of the function

f(x) = \(\begin{cases} x+1, & \quad x≥1\\ x^2+1, & \quad x<1 \end{cases} \)

Answer 1

In both the intervals x = 1 and x < 1 the function f(x) is a polynomial so continuous. So we have to check the continuity at x = 1.

f(1) = 2
Since

f(x) is continuous at x = 1.