f of x equals the quantity x minus one times the quantity x plus two times the quantity x plus four all divided by the quantity x plus one times the quantity x minus two times the quantity x minus four, Bella and Edward have two different thoughts. Bella says that the function is defined at x = –1, x = 2, and x = 4. Edward says that the function is undefined at those x values. Who is correct? Justify your reasoning.

[tex]f(x)=\frac{(x-1)(x+2)(x+4)}{(x+1)(x-2)(x-4)}[/tex]

The denominator of a fraction can't be equal to 0.
[tex](x+1)(x-2)(x-4) \not= 0 \\ x+1 \not=0 \ \land \ x-2 \not= 0 \ \land \ x-4 \not= 0 \\ x \not= -1 \ \land \ x \not = 2 \ \land \ x \not= 4[/tex]

The function is undefined at x=-1, x=2, x=4, because for these values the denominator of the function would equal 0, and it's impossible to divide by 0.

Edward is correct.

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