Question

What are the discontinuities of the function f(x) = x^2+5x+6/2x+16

Answer 1

The discontinuity of the function is at x=-8.

Explanation:

Given : Function
`f(x)=(x^2+5x+6)/(2x+16)`

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,

`f(x)=(x^2+5x+6)/(2x+16)`

`f(x)=((x+2)(x+3))/(2(x+8))`

Denominator = 0

`2(x+8)=0`

`x+8=0`

`x=-8`

The discontinuity of the function is at x=-8.

Answer 2

As written (without grouping symbols), there are no discontinuities.

If you mean ...

`f(x)=(x^(2)+5x+6)/(2x+16)`
it will have a discontinuity where the denominator is zero, at x=-8.