How do you find the domain of #f(x) = (x+9)/(x^2-361)#?

2 Answers
May 31, 2018

Answer:

The domain is #x in (-oo,-19)uu(-19,19)uu(19,+oo)#

Explanation:

The denominator must be #!=0#

Therefore,

#x^2-361!=0#

#x^2!=361#

#x!=sqrt(361)#

#x!=19# and #x!=-19#

The domain is #x in (-oo,-19)uu(-19,19)uu(19,+oo)#

graph{(x+9)/(x^2-361) [-36.53, 36.52, -18.28, 18.27]}

May 31, 2018

Answer:

#x inRR,x!=+-19#

Explanation:

The denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator to zero and solving gives the values that x cannot be.

#"solve "x^2-361=0rArrx=+-19larrcolor(red)"excluded values"#

#"domain "x inRR,x!=+-19#

#"this can be expressed in "color(blue)"interval notation"#

#x in(-oo,-19)uu(-19,19)uu(19,oo)#
graph{(x+9)/(x^2-361) [-40, 40, -20, 20]}