Question

Is it possible to find the values of y for which y-4/y^2-4y-12 is undefined? Justify your answer.​

Answer 1

y =10

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Given:

$\frac{y - 4}{ {y}^{2} - 4y - 12}$

To find: Find the values of y for which the given function is undefined? Justify your answer.

Solution:

Tip: A function in p(y)/q(y) form is undefined when q(y) =0, for some value of y.

Step 1: Factorise the denominator.

${y}^{2} - 4y - 12 \\ \\ {y}^{2} - 6y + 2y - 12 \\ \\ y(y - 6) + 2(y - 6) \\ \\{y}^{2} - 4y - 12 = (y - 6)(y +2)$

Step 2: Find the zeros of denominator.

$y - 6 = 0 \\ \\ y = 6 \\ \\ y + 2 = 0 \\ \\ y = - 2$

Step 3: On putting y=6 or y=-2,

the function becomes undefined.

In order to justify the statement,

put y=6

$\frac{y - 4}{ {y}^{2} - 4y - 12} = \frac{y - 4}{(y - 6)(y + 2)} \\ \\ = \frac{6 - 4}{(6 - 6)(6 - 2)} \\ \\ = \frac{2}{0 \times 4} \\ \\ = \frac{2}{0} \\ \\ = undefined$

By the same way, it can be justified for y=-2.

Final answer:

For y=6, -2, the given function is undefined.

Hope it helps you.

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