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