Question

What is the restriction of the equation 4y(8y+24)^-1

My choices are either y cannot equal +3
or y cannot equal -3

Answer 1

y cannot equal -3.

Explanation:

Rewrite 4y(8y+24)^-1 to make it more obvious that this is a rational quantity:

4y 4(y) y

-------------- = ---------- = ------------

(8y+24)^1 8(y+3) 2(y+3)

The only y value for which this function is undefined is y = -3. At that value of y, the fraction is undefined due to division by zero.

Thus, the correct answer is "y cannot equal -3."

Answer 2

y cannot equal -3

Explanation:

The denominator in this rational expression must not become zero, so:

`(4y)/(8y+24)\,,\,\,\,8y+24\\eq 0\implies y\\eq -3`