Inverse Functions

 

 

Course : 

 

For Pre-calculus students

Created by Kameswari Tekumalla for Synergy Project (Mar 6th)

Uses Web links produced by StefanWaner, Steven R. Costenoble,

Dan Rinneand, and Lawrence S. Husch.

 

 

Background:

 

An invertible function, as the name implies, is a function that can be inverted.

An invertible function must satisfy the condition that different inputs in the domain correspond to different outputs. That is, all of the elements in the domain and range are paired-up in monogamous relationships - each element in the domain pairs with only one element in the range, and each element in the range pairs with only one element in the domain inverse functions. Click here for the exercise set for this topic.  Thus, the inverse of a function is a function that looks at this relationship from the other viewpoint.  So, for all elements a in the domain of f(x), the inverse of f(x) (notation: f^-1(x)) satisfies: f (a) = b implies f^-1(b) = a.  For more details and to view the graphing utility, click Definition& existence of inverse function. To know how to find the formula for inverses, go to Formula for inverse function. Take a Drill for finding inverses.

 

 

QUESTIONS:

 

Q1.  Show that the following functions are inverses to each other and

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Q2.  Determine whether f(x) = 7 has inverse or not? If yes, find it?

 

 

 

Q3. Determine whether f(x) =  x⁴ - x² has inverse or not? If yes, find it?

 

 

 

 

Q4.  Find the inverse f(x) = (3x+4)/5.

 

 

 

 

 

 

 

Q5.  Cellular Phones: From 1987 to 1996 the average local phone bills decreased. A

        function that approximates the average phone bill per month is y = 141.919 –

       6.05503t, 0£ t £16, where y represents the amount of the bill in dollars, and t = 7 

        represents 1987.  Find the inverse of this function, and use f^-1 to find the year with 

        the monthly bill of $51.00 (Source: Cellular Telecommunications Industry

        Association)