Question

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

Answer 1

The domain of `f(x)` is `RR-{-3}`

Explanation:

As you cannot divide by `0`, the denominator must be `!=0`

Therefore,

`x+3!=0`

`x!=-3`

The domain of `f(x)` is `RR-{-3}`

graph{(x-2)/(x+3) [-10, 10, -5, 5]}

Answer 2

`x inRR,x!=-3`

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 value that x cannot be"`

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

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