Respuesta :

InesWalston

Answer-

[tex]The \ inverse \ of \ (x-4)^{2}-\frac{2}{3} =6y-12 \ is \ y= 4\pm \sqrt{6x-\frac{34}{3}}[/tex]

Solution-

The given function,

[tex](x-4)^{2}-\frac{2}{3} =6y-12[/tex]

The inverse of a function normally means switching the role of the variables. ( y becomes the input or independent variable, and x becomes the output or the dependent variable)

Switching x and y, the function becomes,

[tex](y-4)^{2}-\frac{2}{3} =6x-12[/tex]

[tex]\Rightarrow (y-4)^{2}= 6x-12 +\frac{2}{3}=6x-\frac{34}{3}[/tex]

[tex]\Rightarrow (y-4)= \pm \sqrt{6x-\frac{34}{3}}[/tex]

[tex]\Rightarrow y= 4\pm \sqrt{6x-\frac{34}{3}}[/tex]

MrRoyal

The inverse of a function is its opposite

The inverse of the equation is y = 4 + [tex]\sqrt{[/tex]18x-34

The equation is given as:

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

Swap the positions of x and y

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

Multiply through by 3

(y-4)^2-2=18x-36

Add 2 to both sides

(y-4)^2=18x-34

Take the square roots of both sides

[tex]y-4=\sqrt{18x-34}[/tex]

y-4=[tex]\sqrt{[/tex]18x-34

Add 4 to both sides

y = 4 + [tex]\sqrt{[/tex]18x-34

Hence, the inverse of the equation is y = 4 + [tex]\sqrt{[/tex]18x-34

Read more about inverse equations at:

https://brainly.com/question/8120556

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