I'm having some trouble with this question: Find a value(s) that makes the expression y^2 - 16/ y^2 - 16 undefined.
I know that for an expression to be undefined that the denominator must be 0, so I thought -8^2, but that would just result in 16 + 16. I'm really confused and my textbook didn't have any problems like this one.
Yes that sounds right.
yes, but also y = -4i
I meant 4^2
I meant -4^2 not -8^2
(y^2 - 16)/(y^2 - 16) Now since both expressions are the same, set one equal to zero and solve for y. by the way in your explanation you multiplied by 2, but I think you meant to square it instead. I can check your answer if u reply it as well
Im so sorry, again, I meant to write y^2 - 16/ y^2 + 16.
same rules apply solve for the denominator by setting equal to zero, if that doesnt work ill try working it too
Ohhh. I started thinking back to other problems I've done, and I believe that y=4i?
(y^2-16)/(y^2-16) = (y+4)(y-4)/(y+4)(y-4).
Let y + 4 = 0, Y = -4.
Let y-4 = 0, Y = 4.
When Y = -4, (-4+4)(-4-4)/(-4+4)(-4-4) = (0)(-8)/(0)(-8) = 0/0 = undefined.
When Y = 4, Repeat the above operations.
To find the value(s) that make the expression undefined, we need to identify values that would make the denominator equal to zero.
In this case, the expression is (y^2 - 16) / (y^2 - 16). As you correctly mentioned, the denominator must be zero for the expression to be undefined.
To solve for when the denominator is equal to zero, we set it as an equation:
y^2 - 16 = 0
To further solve this equation, we can factor it:
(y - 4)(y + 4) = 0
This equation tells us that the expression will be undefined when either (y - 4) = 0 or (y + 4) = 0.
Solving for each equation:
1. (y - 4) = 0: Adding 4 to both sides gives us y = 4.
2. (y + 4) = 0: Subtracting 4 from both sides gives us y = -4.
Therefore, the values of y = 4 and y = -4 will make the expression y^2 - 16 / y^2 - 16 undefined. These values result in a denominator of zero, which is not allowed in mathematical operations.