How Do You Calculate f(1/x) and f(x+y) for f(x) = 1/(1+x)?

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Homework Help Overview

The problem involves evaluating the function f(x) = 1/(1+x) at specific arguments, namely f(1/x) and f(x+y). Participants are exploring how to approach these evaluations and the implications of the function's structure.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the nature of substituting different expressions into the function, questioning whether f(1/x) represents an inverse or simply a substitution. There is also consideration of how to handle the variable y in f(x+y) and whether it can be treated like a constant.

Discussion Status

Some participants have provided guidance on how to approach the substitutions, suggesting that the process is similar to evaluating the function at specific numerical values. There is an ongoing exploration of the correctness of the expressions derived for f(x+y) and f(1/x), with some participants expressing uncertainty.

Contextual Notes

There is a lack of specified values for y, which has led to some confusion among participants regarding the evaluation of f(x+y). Additionally, the original poster expresses uncertainty about the implications of the substitutions.

potmobius
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1. Let f(x) = 1/(1+x). What is:
a. f(1/x)
b. f(x+y)





The Attempt at a Solution


Frankly, I have no idea how to do this. But does the first one mean the inverse of the original function? and for the second one, no value for "y" is specified. So I'm lost...
 
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Hi potmobius,

What would you have done if the question instead asked for f(5) or f(0)?

It is no different for these questions. Simply plug in the argument (in this case 1/x and x+y) into where x is.
 
How would you find f(1)? Plug in 1 for x. How would you find f(2)? Plug in 2 for x. How would you find f(3)? Plug in 3 for x. So how would you find f(1/x) and f(x+y)?
 
okay, i think i understand the f(x+y) part... but i still have some doubt about f(1/x). Do i treat the (1/x) part as just another variable, like y, for instance?
---------------------------------------------------------------
for the f(x+y) part, i did it like this:

f(x+y) = 1/(1+x+y)

is it correct? is that all there is to it?
 
for f(1/x) i got f(1/x) = x/(x+1)

is that correct?
 
Yes, this is correct potmobius.
 
Thanks a lot Coto! That really cleared up things! :biggrin:
 

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