Question

Specify the domain of the function.

y=1/2^x-1

Answer 1

Okay multiply by 2, what do you get?

Answer 2

Should be 2y = 2/2^x-1

Answer 3

2 is the same as 2^1 right?

Answer 4

Now you have the same base for your numerator and denominator

Answer 5

So, business as usual 2^1/2^x-1 = 2^1-(x-1).
Remember to distribute the negative.

Answer 6

why would i multiply by 2 ?

Answer 7

sorry the -1 is not with the x

Answer 8

it is 2^x -1

Answer 9

so its
y = (.5^x) - 1
?

Answer 10

yes

Answer 11

To give your numerator the same base as your denominator - so that you can use your subtraction rule.

Answer 12

You use that subtraction rule to get it out of the denominator, so that you no longer have a fraction.

Answer 13

Okay yea that changed it lol, one sec

Answer 14

i know that it is not all real numbers

Answer 15

is it negative infinite to 0 then 0 to infinite

Answer 16

not including zero

Answer 17

Yes, otherwise whatever the base is would be 1^10 instead of .5^x

Answer 18

thanks

Answer 19

Okay got it.

Answer 20

yes

Answer 21

y= (1/2)^x -1

y-1 = (1/2)^x

y-1 = 1^x/2^x (1 to any power is still 1 - 1x1x1=1)

y-1 = 1/2^x

y-1 = 2^-x

Now we take the log (base of the exponent) of the other side of the equation. This takes the x out of the exponent.

-x = log<base2>(y-1)

x = -log<base2>(y-1)

Answer 22

Magic!

Answer 23

thanks i was just looking for the interval notation