Question

How do you find the domain of the function `F(x)= -4/(3x^2-5x-2)`?

Answer 1

`(-oo,-1/3)uu(-1/3,2)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 "3x^2-5x-2=0rArr(3x+1)(x-2)=0`

`3x+1=0rArrx=-1/3larrcolor(red)"excluded value"`

`x-2=0rArrx=2larrcolor(red)"excluded value"`

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