Answer:
The correct option is D.
Step-by-step explanation:
The given function is
\(f(x)=\frac{x^2+6x+9}{3x+15}\)
\(f(x)=\frac{x^2+2(x)(3)+3^2}{3(x+5)}\)
Using algebraic property:
\((a+b)^2=a^2+2ab+b^2\)
\(f(x)=\frac{(x+3)^2}{3(x+5)}\)
\(f(x)=\frac{(x+3)(x+3)}{3(x+5)}\)
A rational function is discontinuous at that point where the value of denominator equal to 0.
Equate denominator equal to 0.
\(3(x+5)=0\)
\(x+5=0\)
\(x=-5\)
Therefore function is discontinuous at \(x=-5\).
The discontinuity of the function is
\(x
eq -5\)
The function f(x) is not defined at \(x=-5\).Therefore option D is correct.
