which equation is the inverse of $(x - 4)^2-\frac{2}{3}=6y - 12$?\n$y=\frac{1}{6}x^{2}-\frac{4}{3}x+\frac{43}…

which equation is the inverse of $(x - 4)^2-\frac{2}{3}=6y - 12$?\n$y=\frac{1}{6}x^{2}-\frac{4}{3}x+\frac{43}{9}$\n$y = 4pmsqrt{6x-\frac{34}{3}}$\n$y=-4pmsqrt{6x-\frac{34}{3}}$\n$-(x - 4)^2-\frac{2}{3}=-6y + 12$

which equation is the inverse of $(x - 4)^2-\frac{2}{3}=6y - 12$?\n$y=\frac{1}{6}x^{2}-\frac{4}{3}x+\frac{43}{9}$\n$y = 4pmsqrt{6x-\frac{34}{3}}$\n$y=-4pmsqrt{6x-\frac{34}{3}}$\n$-(x - 4)^2-\frac{2}{3}=-6y + 12$

Answer

Explanation:

Step1: Intercambiar x e y

Dada la ecuación ((x - 4)^2-\frac{2}{3}=6y - 12), intercambiamos (x) e (y) para obtener ((y - 4)^2-\frac{2}{3}=6x - 12).

Step2: Despejar y

Comenzamos por aislar el término con ((y - 4)^2): ((y - 4)^2=6x - 12+\frac{2}{3}). Calculamos (6x - 12+\frac{2}{3}=6x-\frac{36}{3}+\frac{2}{3}=6x-\frac{34}{3}). Luego, tomamos la raíz cuadrada de ambos lados: (y - 4=\pm\sqrt{6x-\frac{34}{3}}). Finalmente, despejamos (y): (y = 4\pm\sqrt{6x-\frac{34}{3}}).

Answer:

(y = 4\pm\sqrt{6x-\frac{34}{3}}) (segunda opción)