Answer:
The discontinuity of the function is at x=-8.
Step-by-step explanation:
Given : Function [tex]f(x)=\frac{x^2+5x+6}{2x+16}[/tex]
To find : What are the discontinuities of the function?
Solution :
Discontinuity of the function is happen when denominator is zero.
First we factor the function,
[tex]f(x)=\frac{x^2+5x+6}{2x+16}[/tex]
[tex]f(x)=\frac{(x+2)(x+3)}{2(x+8)}[/tex]
Denominator = 0
[tex]2(x+8)=0[/tex]
[tex]x+8=0[/tex]
[tex]x=-8[/tex]
The discontinuity of the function is at x=-8.
