finding domain?

Question

what is the domain of this:

ln [(8x+7)/(2-22x)]

Answer 1

When (8x+7)/(2-22x)>0
or when 8x+7>0 and 2-22x>0
-7/8 or when 8x+7<0 and 2-22x<0
2/11

Answer 2

inside of ln > 0, bottom of fraction =/= 0

so

8x + 7 < 0 & 2 - 22x < 0, or 8x + 7 > 0 & 2 - 22x > 0

x < -7/8 & x > 1/11 or x > -7/8 & x < 1/11

the only valid one of these is -7/8 < x < 1/11

To show that x < -7/8 won't work, lets choose a value for x, say -1.

Then we get ln[(-8 + 7) / (2 + 22)]

= ln[-1/24]

which doesn't exist

Similarly for x > 1/11, let x = 1

ln[(8 + 7)/(2 - 22)]

= ln[-3/4] which also doesn't exist

Answer 3

this is incomplete question, you should have told me the range of x like : 6 well I will show you the method.
take x to be 1
then y=[(8*1+7)/(2-22*1)]
=[(8+7)/(2-22)]
=[15/-20]
this is your range for x=1
do this for varying x values