Inverse of a quadratic function

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.

Re: Inverse of a quadratic function

Quote:

Originally Posted by

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

To talk about the inverse function, the original function f(x) = 2x^{2 }+ 8x - 7 must be injective. However, a quadratic polynomial considered as a function on all real numbers is not injective because a horizontal line can intersect the graph in two points. In particular, there are two values of x for which f(x) = 2.

Quote:

Originally Posted by

**barbiedise** 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.

The discriminant is 64 + 72.

Quote:

Originally Posted by

**barbiedise** 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.

This needs more context. Inverse of what and what is or is not an inverse? I am not sure what the connection is with testing for a perfect square. A question whether some n is a perfect square is a question about the existence of an integer (whose square is n), but the quadratic formula accepts and returns real numbers in general.

Quote:

Originally Posted by

**barbiedise** Also would like to know if it is bijective.

As a function from all reals to all reals, no quadratic polynomial is either injective (because the graph has two branches) or surjective (because the function has a minimum or a maximum).