Question

Examine the following function for continuity:

f(x) = x – 5

Answer 1

Let a be a real number, then,

`lim_(x->a^+)` f(x) = `lim_(h->0)` (a + h) − 5 = a − 5

`lim_(x->a^-)` f(x) = `lim_(h->0)` (a − h) − 5 = a − 5

Also f(a) = a − 5

∵ `lim_(x->a^+)` f(x) = `lim_(x->a^-)` f(x) = f(a)

Hence, the given function f(x) = (x − 5) is continuous.