The discussion revolves around the function f(x) = x^5 - x^3 + 2x and its invertibility. Participants are tasked with demonstrating the function's invertibility and computing the derivative of its inverse at a specific point.
The discussion is ongoing, with participants exploring the conditions necessary for a function to be invertible. Some guidance has been offered regarding the need to demonstrate that the function is increasing, but there is no explicit consensus on the approach to take.
Participants are navigating the requirements of the homework prompt, which asks for proof of invertibility rather than the actual computation of the inverse. There is a focus on understanding the implications of the function's derivative.
Lucky for you, you weren't asked to calculate ##f^{-1}##, just show it exists. Can you show, for example, that ##f## is increasing?alexs2jennisha said:Homework Statement
1. Show that the function f(x) = x5 -x3 +2x is invertible. Compute the derivative of f-1
at 2.
The Attempt at a Solution
To find f-1 I switched x and y which gave me x = y5 - y3 + 2y
this is where i got stuck because I am not sure how to solve for y after that step.
Can the y5 - y3 become y2?
alexs2jennisha said:Can the y5 - y3 become y2?