Question

Examine the continuity of the following function :

`{:(,f(x),=(x^2-16)/(x-4),",","for "x!=4),(,,=8,",","for "x=4):}} " at " x=4`

Answer 1

`f(x) = (x^2-16)/(x-4),` for x ≠ 4

 = 8     for x = 4

f(4) = 8

Now `lim_(x-> 4)f(x) = lim_(x-> 4) (x^2-16)/(x-4)`

`= lim_(x-> 4)((x-4)(x+4))/(x-4)`

= 8

Thus `lim_(x-> 4)f(x) = f(4)=8`

Hence function `f` is continuous at x = 4.