Question

How do you find the domain of `f( x ) = \frac { x + 3} { x ^ { 2} + 5x - 4}`?

Answer 1

`(-oo,-4)uu(-4,-1)uu(-1,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+5x+4=0rArr(x+4)(x+1)=0`

`rArrx=-4,x=-1larrcolor(red)"are excluded values"`

`x in(-oo,-4)uu(-4,-1)uu(-1,oo)`
graph{(x+3)/(x^2+5x+4) [-10, 10, -5, 5]}