Question

In Problem, determine whether f is continuous at c.

$f\left(x\right)=\frac{x^2-4}{x+2},c=-2$

Short answer

The given polynomial function$f\left(x\right)=\frac{x^2-4}{x+2},c=-2$
is not continuous at c = 5

Step-by-step solution

Step1. Given information 

Polynomial function $f\left(x\right)=\frac{x^2-4}{x+2},c=-2$

c=-2

We know that

A function is called continuous function when at x= a,

$\underset{x\to a}{lim}f\left(x\right)=f\left(a\right)$

and defined for every number of domain

Step2. Calculations of continuity 

According to the question, given function is a rational function, To find the domain of function firstly we have to find the value of x, where the denominator gets 0

at x=-2 , (x+2) gets 0

so the domain of the function is $x\in (R-(-2\left)\right)$

As -2 is not in the domain

so we cant find continuity at -2

• the given function is continuous at x= -2