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

1 Answer
Jammin Bay · Stefan V.
Oct 19, 2015

#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#

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