Finding Inverses of F(x) on Restricted Intervals

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Homework Help Overview

The discussion revolves around finding the inverses of the function F(x) = x + 1/x on specified restricted intervals. Participants are exploring how to approach the problem of determining the inverse function based on the graph and its behavior across different intervals.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the need to express x in terms of y for the function F(x) and question how to proceed after sketching the graph. There is an emphasis on understanding the implications of restricting the domain to specific intervals.

Discussion Status

Some participants have acknowledged the need to solve for x in terms of y and are considering how to represent the solution as a function g(y). There is an ongoing exploration of which intervals allow for g to be a well-defined function.

Contextual Notes

Participants are working under the constraints of the problem statement, which specifies four intervals for the domain restriction and the requirement to find inverse formulas for each interval.

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Homework Statement


Let F(x)=x + 1 / x

a.) sketch graph
b.)From the Graph, it appears that f(x) becomes 1:1 when we restrict its domain to each of the four intervals (-infinity, -1], [-1,0), (0,1] and [1, infinity). For Each of these intervals, find a formula for the inverse of f(x) restricted to the interval.


Homework Equations



Well i sketched the graph which is 2 asymptotes in the X and Y Direction in quadrant 1 and 3... but where do i go from here? i really don't understand the question... just need some help as to where i start and where i end... thank you.



The Attempt at a Solution

 
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The question is, can you express x in terms of y by solving y = F(x), for each of the intervals?
 
Yes You can solve x in terms of y...sorry i don't know what to do next
 
Last edited:
Solve x in terms of y. I will represent the solution as x = g(y), where g(y) is for you to find. Then see over which intervals (on the x axis) g is a well-defined function. (That is, make sure that g is defined over each of the four subintervals.)
 
Last edited:

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