Question

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

Answer 1

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}`