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).
