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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.

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\(f(x)=\frac{(x-1)(x+2)(x+4)}{(x+1)(x-2)(x-4)}\)

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

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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