what is the inverse of 3x^2-5x-2

Question

please show all work!

 

Answer 1

Given function f(x) = 3x^2-5x-2

y = 3x^2-5x-2

Interchange x and y.

x = 3y^2-5y-2

Subtract x from each side.

3y^2-5y+(-2-x) = 0

To find inverse solve for y.

Compare it to quadratic equation ax^2+bx+c = 0

a = 3, b = -5, c = -2-x

y = [-b±√(b^2-4ac)]/2a

y = [5±√(25-12(-2-x)]/6

y = [5±√(25+24+12x)]/6

y = [5±√(49+12x)]/6

The inverse of the quadratic is the curve formed by the union of the following two functions.

y = [5+√(49+12x)]/6 and y = [5-√(49+12x)]/6