An invertible polynomial is a polynomial function that has an inverse function. This means that for every input, there is a unique output, and for every output, there is a unique input. In other words, the polynomial can be "reversed" or "undone" by its inverse function.
A polynomial is invertible if and only if it is a one-to-one function, meaning that it passes the horizontal line test. This can be determined by graphing the polynomial or by checking the values of its coefficients.
The domain of an invertible polynomial is the set of all real numbers, denoted as P2 (R). The range is also P2 (R), which represents the set of all possible outputs of the polynomial function.
To find the inverse of an invertible polynomial, you can use the process of polynomial long division. This involves dividing the polynomial by x and then swapping the positions of the coefficients. The resulting polynomial is the inverse function.
Yes, an invertible polynomial can have a degree higher than 2. The degree of the polynomial does not affect its invertibility, as long as it is a one-to-one function. However, the notation P2 (R) specifically refers to polynomials of degree 2.