Question

Examine the following function for continuity:

f(x) = |x – 5|

Answer 1

Let f(x) = |x – 5|

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

= |a − 5|

= a − 5

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

= |a − 5|

= a − 5

f(a) = |a − 5| = a − 5

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

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