Find the inverse of f(x)= 3x^2+2xI would like to know the steps to perform this problem, thanks in advance!

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jeew-m | College Teacher | (Level 1) Educator Emeritus

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`f(x)= 3x^2+2x`

`y = 3x^2+2x`

Usually y term of a equation is called the dependent variable and the x terms are called independant variables. y is changing according to x.

When finding inverse what we do is we replace or change these variables. In other words x becomes dependant and y becomes in dependant.

 

`y = 3x^2+2x`

`3x^2+2x = y`

`3x^2+2x-y = 0`

 

So now we have to complete the square.

`3x^2+2x-y = 0`

`3(x^2+(2x)/3-y/3) = 0`

`x^2+(2x)/3-y/3 = 0`

`(x+1/3)^2-y/3-1/9 = 0`

`(x+1/3)^2 = y/3+1/9`

   ` (x+1/3) = +-sqrt(y/3+1/9)`

              `x = -1/3+-sqrt(y/3+1/9)`

 

So the inverse function is;

`x = -1/3+-sqrt(y/3+1/9)`

 

Usually we place y as dependant and x as in dependant. So we can write the inverse function as;

`y = -1/3+-sqrt(x/3+1/9)`

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