inverse function of x^2 -3x+2

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Answer 1

let y = x²-3x+2

 

The inverse function should be written as x = f(y), so we need to solve for x in terms of y.

 

y-2 = x²-3x

 

Complete the square on the right.

 

Write as: y-2 = x² - 2 * 3/2 x

         

(x-3/2)² = x² - 3x + 9/4

 

x² - 3x = x² - 3x + 9/4 - 9/4 = (x-3/2)² - 9/4

 

Replace this above:

 

y-2 = (x-3/2)² - 9/4

y-2+9/4 = (x-3/2)²

y+1/4 = (x-3/2) ²

 

Take square root of both sides:

 

(y+1/4)^1/2 = x-3/2

 

SO THE INVERSE FUNCTION IS:

x = (y+1/4)^1/2 + 3/2