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When looking at the rational function 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.

Verified Answer :

scme1702

f(x) = [(x-1)(x+2)(x+4)] / [(x+1)(x-2)(x-4)]
The function shows discontinuity at those values of x as the denominator becomes 0; therefore, Edward is correct.

Answer:

Edward is correct

Step-by-step explanation:

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

When denominator =0 , then the function becomes undefined

Now we look at the values of x that makes the denominator 0

We set the denominator =0  and solve for x

(x+1)(x-2)(x-4) =0

x+1=0 so x= -1

x-2=0 so x=2

x-4 =0 so x=4

x=-1 , 2 and 4 makes the denominator 0. that is undefined

So Edward is correct