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

Answer-

Solution-

The given function,

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,

The inverse of a function is its opposite

The inverse of the equation is y = 4 + 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

y-4=18x-34

Add 4 to both sides

y = 4 + 18x-34

Hence, the inverse of the equation is y = 4 + 18x-34

Read more about inverse equations at:

link

-4x = -3

3 = 4x