Question

How do you find the domain of `f(x) = (x+7)/(x^2-4)`?

Answer 1

`(-oo,-2)uu(-2,2)uu(2,oo)`

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^2-4=0rArrx^2=4`

`rArrx=-2,x=2larrcolor(red)"excluded values"`

`rArr"domain "(-oo,-2)uu(-2,2)uu(2,oo)`
graph{(x+7)/(x^2-4) [-10, 10, -5, 5]}