Provide an appropriate response.Why does a quadratic function never have an inverse?

Question

What will be an ideal response?

Answer 1

Quadratic functions are of the form  Two different x-coordinates will produce the same value for (x + a)², at every value of x except -a, so a quadratic function will clearly fail the horizontal line test. Therefore, a quadratic function is not one-to-one and thus has no inverse.