How do you determine the domain of #f( x ) = \frac { x ^ { 2} + x - 6} { x ^ { 2} - 3x - 40}#?

1 Answer
May 1, 2018

Let be #g(x)=x^2+x-6# and #h(x)=x^2-3x-40# then

#f(x)=g(x)/(h(x))#

Dom g(x) is all #RR# because there is no restriction in numerator

Dom h(x) will be all reals number except those that make zero this expresion

#x^2-3x-40=0# #x=(3+-sqrt(9+160))/2=(3+-13)/2# which solutions are #x=8# and #x=-5#

Then Dom f(x)=#RR-{-5,8}#