Respuesta :
Answer:
The correct option is option B.
Step-by-step explanation:
The given function is
[tex](x - 4)^{2} - \frac{2}{3} = 6y - 12[/tex]
We can rearrange the function as
[tex](x - 4)^{2} - \frac{2}{3} = 6y - 12[/tex]
⇒ 3(x - 4)² - 2 = 18y - 36
⇒ 3(x - 4)² = 18y - 34
⇒ [tex](x - 4)^{2} = 6y - \frac{34}{3}[/tex]
⇒ [tex]x - 4 = \pm \sqrt{6y - \frac{34}{3}}[/tex]
⇒ [tex]x = 4 \pm \sqrt{6y - \frac{34}{3}}[/tex]
Therefore, the inverse function will be, [tex]y = 4 \pm \sqrt{6x - \frac{34}{3}}[/tex]
Therefore, the correct option is option B. (Answer)
The inverse of the equation [tex](x - 4)^2 - \frac 23 = 6y -12[/tex] is [tex]y = 4 + \sqrt{6x -\frac{34}3[/tex]
What is an inverse equation?
An inverse equation is the opposite of the original equation
The equation is given as:
[tex](x - 4)^2 - \frac 23 = 6y -12[/tex]
To determine the inverse, we start by swapping the positions of x and y
[tex](y - 4)^2 - \frac 23 = 6x -12[/tex]
Add 2/3 to both sides
[tex](y - 4)^2 = 6x -12 + \frac 23[/tex]
This gives
[tex](y - 4)^2 = 6x -\frac{34}3[/tex]
Take the square root of both sides
[tex]y - 4 = \sqrt{6x -\frac{34}3[/tex]
Add 4 to both sides
[tex]y = 4 + \sqrt{6x -\frac{34}3[/tex]
Hence, the inverse of the equation [tex](x - 4)^2 - \frac 23 = 6y -12[/tex] is [tex]y = 4 + \sqrt{6x -\frac{34}3[/tex]
Read more about inverse equations at:
https://brainly.com/question/9289171
