How do you find the domain for #H(x) = [(x - 1) (x + 2) (x - 3)]/(x(x - 4)^2)#?

1 Answer
Jul 6, 2018

Answer:

#(-oo,0)uu(0,4)uu(4,oo)#

Explanation:

The denominator of h(x) cannot be zero as this would make h(x) undefined. Equating the denominator to zero and solving gives the values that x cannot be.

#"solve "x(x-4)^2=0#

#rArrx=0" and "x=4larrcolor(red)"excluded values"#

#"domain "x in(-oo,0)uu(0,4)uu(4,oo)#
graph{((x-1)(x+2)(x-3))/(x(x-4)^2) [-10, 10, -5, 5]}