Precalc question

Question

For this problem, y = f(x) = 2x^2 − 3x − 1 on the domain of all real numbers.

Explain why y = f(x) does not have an inverse function on the domain of all real numbers.

Answer 1

This can be explained by simply looking at the graph----but I suspect you need more than that.

In general, any equation where the dominant term is an even exponent will not have an inverse covering all real values.

With y = x² , there is an answer for every x value. The inverse is x = √y, which has a real solution only for x≥0