How do you find the domain for #f(q)=(q+1)/(q^2+6q-27)#?

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Answer 1 · 2018-07-05T11:57:22

The domain is #q in (-oo, -9) uu(-9,3)uu(3,+oo)#

The denominator is

#q^2+6q-27=(q-3)(q+9)#

As the denominator must be #!=0#

#(q-3)(q+9)!=0#

#{(q-3!=0),(q+9!=0):}#

#=>#, #{(q!=3),(q!=-9):}#

The domain is #q in (-oo, -9) uu(-9,3)uu(3,+oo)#

graph{(x+1)/(x^2+6x-27) [-20.28, 20.26, -10.14, 10.14]}