How do you find the domain and range of f(x) = (x+3 )/ (x^2 + 8x + 15)f(x)=x+3x2+8x+15?

1 Answer

x != -3, -5x3,5
Or is can be written as (-oo , -3) uu (-3, -5) uu (-5, oo)(,3)(3,5)(5,)
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 x2+8x+15

15/3 =5153=5

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

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

x =-3, x = -5x=3,x=5

Since the denominator cannot be zero, since 0/0 = "Err"00=Err,
The domain is x != -3, -5x3,5