Question

Given the domain(-4,0,5), what is the range for the relation 12x×6y=24?

Answer 1

Answer:

The range is $(-\frac{1}{12} ,\frac{1}{15})$. The realtion is no defined in 0.

Step-by-step explanation:

Given the domain(-4,0,5)

For x=-4

12x×6y=24

12(-4)×6y=24

-48×6y=24

6y=$\frac{24}{-48}$

y=$\frac{-1}{2*6}$

y=$\frac{-1}{12}$

For x=0

The relation is not defined

For x=5

12x×6y=24

12(5)×6y=24

60×6y=24

6y=$\frac{24}{60}$

y=$\frac{2}{5*6}$

y=$\frac{1}{15}$

Answer 2

Answer:

The range has only two elements:

$-\frac{1}{12}$

$\frac{1}{15}$

Step-by-step explanation:

The range is the y set of number that are images of x. So, to find each range, we only need to replace each x value and find y.

$x = -4\\12x6y=24\\12(-4)6y= 24\\y=\frac{24}{-288}\\y = -\frac{1}{12}$

$x = 0\\12x6y=24\\y= \frac{24}{72x} \\y= \frac{24}{0}=\inf$

$x=5\\y= \frac{24}{72x}\\y= \frac{24}{72(5)}=\frac{24}{260}=\frac{1}{15}$

Therefore, the range of the given domain is $-\frac{1}{12}$ and $\frac{1}{15}$, the set has only two elements be cause x = 0 is undetermined, it doesn't have an image in y set.