Question

What is the discontinuity of the function f(x)=x^2-3x-28/x+4?
A. (-7,-14)
B. (7,0)
C. (4,-3)
D. (-4,-11)

Answer 1

In case that the equation is f(x)=x^2-3x-28/(x+4)
it has a discontinuity issue in x =  -4 due to division by 0 

in this case the option would be
D. (-4,-11) 

Answer 2

Answer:

Option D is correct that is (-4,-11).

Step-by-step explanation:

We have been given an expression:

$f(x)=\frac{x^2-3x-28}{x+4}$

We need to find the points of discontinuity

We will first factorize the given expression

$\frac{x^2-7x+4x-28}{x+4}$

$\Rightarrow \frac{x(x-7)+4(x-7)}{x+4}$

$\Rightarrow \frac{(x+4)(x-7)}{x+4}$

Hence, the point of discontinuity is where denominator gives value zero

So, $x+4=0\Rightarrow x=-4$

Point of discontinuity is -4

hence, after removing the point of discontinuity the function left is:

$f(x)=x-7$

Hence, put x=-4

$f(-4)=-4-7=-11$

Therefore, option D is correct that is (-4,-11).