Question

How do you find the domain of `f(x) = 6/( x-4)`?

Answer 1

`x inRR,x!=4`

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-4=0rArrx=4larrcolor(red)"excluded value"`

`rArr"domain "x inRR,x!=4`

`x in(-oo,4)uu(4,oo)larrcolor(blue)"in interval notation"`
graph{6/(x-4) [-10, 10, -5, 5]}