Inverse of x 4 2 2 3 6y 12

Asked by maham237 @ 13/01/2021 in Mathematics viewed by 324 People

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

Answered by maham237 @ 13/01/2021

Answer-

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

Solution-

The given function,

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

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,

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

$\Rightarrow (y-4)^{2}= 6x-12 +\frac{2}{3}=6x-\frac{34}{3}$

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

$\Rightarrow y= 4\pm \sqrt{6x-\frac{34}{3}}$

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