how do you expand f(x)=4x^3-2x in order to solve for the inverse of f(x)

Question

please explain how to find the inverse function for f(x)

Answer 1

There is no inverse function because all functions require a unique mapping from the domain to the range. That is, if y=g(x) is the inverse function then for some value x=c there can only be a single value g(c). You can't map from a single value of x to more than one value of y. For example, if we solve 4x³-2x=0=2x(2x²-1), we get x=0, x=1/√2, x=-1/√2. Each of these maps to 0, so the inverse would need to map 0 to each of the three values. But a function can only map the domain to a unique value.