Question

Is the function f, defined by f(x)= x^2-5x+4/(x^2-16) , x≠4

f(4)=0, continuous at x=4. Give reasons for your answer.

Answer 1

The function f is continuous at some point c if:

$\displaystyle {\lim_{x\to c} }=f(c)$

In our case:

$\displaystyle {\lim_{x\to 4} }\ne f(4)$

So, the function f(x) is not continuous at x=4