Show that f(x)=4x^5-8x^4 is one to one algebraically. Then find the inverse.

Question

Not necessarily looking for the answer, i just don’t know how to put the problem together

Answer 1

Just looking at the graph, you can see that f(x) is not 1-1.
For example f(-0.559) = f(0.657) = f(1.984) = -1
So it has no single inverse.

For f to be 1-1, it must be monotonically increasing or decreasing. That means that f'(x) is always either positive or negative.