Question

How do you find the domain and range of `f(x) = (x+3 )/ (x^2 + 8x + 15)`?

Answer 1

`x != -3, -5`
Or is can be written as `(-oo , -3) uu (-3, -5) uu (-5, oo)`
you may have been taught to use '[ ]' for included and '] [' for excluding.

Explanation:

You need to simplify the denominator and find where x = 0.

`x^2 +8x + 15`

`15/3 =5`

`(x+3)(x+5)`

`x +3 = 0, x + 5 = 0`

`x =-3, x = -5`

Since the denominator cannot be zero, since `0/0 = "Err"`,
The domain is `x != -3, -5`