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

The inverse of (x-4)^2-2/3 =6y-12 is (24+sqrt(216x-408))/6 ,(24-sqrt(216x-408))/6

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

inverse

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

\frac{24 + 216 x - 408}{6}, \frac{24 - 216 x - 408}{6}

Solution steps

y = \frac{3 x ^{2} - 24 x + 82}{18}

Replace

x

with

y

x = \frac{3 y ^{2} - 24 y + 82}{18}

Solve for

y, x = \frac{3 y ^{2} - 24 y + 82}{18}

\frac{24 + 216 x - 408}{6}, \frac{24 - 216 x - 408}{6}

What is the inverse of (x-4)^2-2/3 =6y-12 ?
The inverse of (x-4)^2-2/3 =6y-12 is (24+sqrt(216x-408))/6 ,(24-sqrt(216x-408))/6