Question

Find the inverse of f(x) = 2x^2 - 3. Explain each step and verify that it is an inverse

Answer 1

the function \[f(x)=2x^2-3\] is not a one to one function since \[f(2)=5\] and \[f(-2)=5\]
in fact the function is even
so unless you restrict the domain somehow, it does not have an inverse

Answer 2

on the graph of \(y=2x^2-3\) lives the points \((2,5)\) and \((-2,5)\)
if you switch the ordered pairs for the inverse you would have \((5,-2)\) and also \((5,2)\) which a function cannot have