Hello everyone, I had to be stuck with a Maths teacher from hell...

I was taught how to get the inverse of the following: 2x^{2 }+ 8x - 7 show at f^{-1}(2)

I understood the computations and interchanging and how it arrived at: 2y^{2 }+ 8y - 9 = 0

However, my teacher used b^{2 }- 4ac to arrive at 64 - 72 = -8, which is where my problem begins.

I would like to know what testing for a perfect square has got to do with the inverse and how it proves it is or isn't an inverse.

Also would like to know if it is bijective.

I would be very greatful for explanations, my teacher doesn't explain anything and i think you guys are way better teachers.

Thank you.