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

[potmobius]

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...

 

[Coto]

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.

 

[Dunkle]

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)?

 

[potmobius]

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?

 

[potmobius]

for f(1/x) i got f(1/x) = x/(x+1)

is that correct?

 

[Coto]

Yes, this is correct potmobius.

 

[potmobius]

Thanks a lot Coto! That really cleared up things!