Question

Which equation is the inverse of (x-4)² - 2/3 = 6y-12 ?

Answer 1

`x=((y-4)^2)/(6)+(17)/(9)`

is the inverse of the function.

Explanation:

We have been given the function:

`(x-4)^2-(2)/(3)=6y-12`

For inverse function we will swap x and y

And firstly, we will find the value of y in terms of x

and then replace x and y

`6y=(x-4)^2-(2)/(3)+12`

`6y=(3(x-4)^2-1+36)/(3)`

`y=((x-4)^2)/(6)+(17)/(9)`

Now, we will replace x and y

`x=((y-4)^2)/(6)+(17)/(9)`

Answer 2

`y=\sqrt{6y-(34)/(3)}+4`

Explanation:

`(x-4)^2-(2)/(3)=6y-12`

In order to find the inverse of above function, we solve it for x in term of y and make the replace x with y in the final answer.

Adding \frac{2}{3} on both hand sides we ger

`(x-4)^2=6y-12+(2)/(3)\\(x-4)^2=6y+(-36+2)/(3)\\(x-4)^2=6y+(-34)/(3)`

`(x-4)^2=6y-(34)/(3)`

Taking square root on both hand sides we get

`(x-4)=\sqrt{6y-(34)/(3)}`

Adding 4 on both sides we get

`x=\sqrt{6y-(34)/(3)}+4`

Replacing x with y and y with x we get

`y=\sqrt{6y-(34)/(3)}+4`