Question

If `c(x) = 5/(x-2)` and `d(x) = x+3`, what is the domain of `(cd)(x)`?

Answer 1

`x inRR,x!=2`

Explanation:

`(cd)(x)=5/(x-2)xx(x+3)=(5(x+3))/(x-2)`

`"the denominator of (cd)(x) cannot be zero as this "`
`"would make it undefined. Equating the denominator"`
`"to zero and solving gives the value that x cannot be"`

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

`rArr"domain is "x inRR,x!=2`