Question

Examine the continuity of the function f(x) = 2x² – 1 at x = 3.

Answer 1

f(x) = 2x² – 1

At x = 3,

`lim_(x -> 3)` f(x) = `lim_(x -> 3)` (2x² – 1)

= 2 × (3)² – 1

= 2 × 9 – 1

= 18 – 1

= 17

f(3) = 2 × (3)² – 1 = 17

`lim_(x -> 3)` f(x) = f(3)

Hence, the function is continuous at x = 3.