Zero and Divisions. In f(x)=27x(3x)x(3x)x9x find the Zero, Undefined, and Indeterminate. Please teach me how?

Answers are:
Zero = 3
Undefined = 2
Indeterminate = 0
I just don't know how to get them.

1 Answer
Jul 19, 2018

For each of these, we need to think about where the zeroes for the numerator and denominator are. Let's explicitly write that

n(x)=(273x)xandd(x)=(3x9)x

Clearly, n(x)=0 when x=0or3 and d(x)=0 when x=0,2.

A zero happens when n(x) is zero and d(x) is some number, so we get 0some number=0.

An undefined value happens whens d(x) is zero and n(x) is some number, so we get some number0 which is undefined.

An indeterminate case is if both d(x) and n(x) are zero, since 00 is indeterminate.

Thinking about all three of these cases, we can easily derive the solution you gave: zero at x=3, undefined at x=2 and indeterminate at x=0.