Question

To make f continuous at x=2 , f(2) should be defined as what value? Justify your answer.

Answer 1

Answer:

To make f continuous at $x=2$, $f(2)$ should be defined $x = 2.$

Step-by-step explanation:

A function, let say $f(x)$, is defined at $x = c$ is continuous at $x = c$

If the limit of $f(x)$ as $x$ approaches $c$ is equal to the value of $f(x)$ at  $x = c$.

Mathematically it is written as:

if

$\lim _{x\to c}\:f\left(x\right)=f\left(c\right)$

then

$f(x)$ is continuous at  $x = c$.

So from the above definition, we conclude that:

To make f continuous at $x=2$, $f(2)$ should be defined $x = 2.$

i.e.

if

$\lim _{x\to 2}\:f\left(x\right)=f\left(2\right)$

then

$f(x)$ is continuous at  $x = 2$.