Question

How do you find the domain of `f(x)=(2x)/((x-2)(x+3))`?

Answer 1

The denominatos can't be zero.

Explanation:

The only contraint is : `(x-2)(x+3)!=0 iff x!=2 and x!=-3`

so the domain is then `D=x in RR-{-3,2}`

Answer 2

`x inRR,x!=-3,2`

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)(x+3)=0`

`rArrx=-3" and " x=2larrcolor(red)" are excluded values"`

`"domain is " x inRR,x!=-3,2`