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?
An inverse function in calculus is a function that reverses the input and output relationship of another function. In other words, if a function takes an input, the inverse function will take the output and vice versa.
To find the inverse of a function in calculus, you can follow these steps: 1) Rewrite the function as y = f(x), 2) Switch the x and y variables, 3) Solve for y, 4) Replace y with f-1(x) to represent the inverse function.
The domain of an inverse function in calculus is the range of the original function, and the range of an inverse function is the domain of the original function. In other words, the x-values of the inverse function will be the y-values of the original function, and vice versa.
No, not all functions have an inverse in calculus. For a function to have an inverse, it must be one-to-one, meaning that each input has a unique output. This can be determined by using the horizontal line test.
To graph the inverse of a function in calculus, you can reflect the points of the original function across the line y = x. This will result in a graph that is a mirror image of the original function's graph. Additionally, the domain and range of the inverse function will be the same as the range and domain of the original function, respectively.