hi

let f(x) = x/(x-1). determine f(f(x)) simplify answer, and find domain/range of f(f(x))

is the question i got.

help please!

also not sure if posted in the right forum?

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- Mar 20th 2012, 11:16 PMtankertertf functions and domain/range
hi

let f(x) = x/(x-1). determine f(f(x)) simplify answer, and find domain/range of f(f(x))

is the question i got.

help please!

also not sure if posted in the right forum? - Mar 20th 2012, 11:29 PMprincepsRe: f functions and domain/range
- Mar 21st 2012, 07:20 AMmastermind2007Re: f functions and domain/range
This might not be exactly true.

The domain of $\displaystyle f(x) = \frac{x}{x-1} $ is $\displaystyle \mathbb{R} \setminus \{1\} $

and its range is really $\displaystyle \mathbb{R} $ (infinity shall be included in the real numbers).

But then again, f(f(x)) has the above mentioned domain (since the image of $\displaystyle f: \mathbb{R} \rightarrow \mathbb{R} $ is $\displaystyle \mathbb{R} $),

and then you map the real numbers again, in the same way, to itself. And again, the value is not defined at x = 1 (you can really not define it there, because

the left and right limits are different).

So I'd say it's a little tricky here and would nevertheless say that the domain is $\displaystyle \mathbb{R} \setminus \{1\} $.

Of course you have as effective function the identity mapping, however since you cannot divide by zero, the simplification holds ONLY IF x is NOT 1.

That's the point.

I may be corrected if I'm wrong, however I think that this is the correct answer. - Mar 29th 2012, 12:51 PMHallsofIvyRe: f functions and domain/range
Yes, mastermind is correct. f(f(x))= (x/(x-1))/(1/(x-1)) for all x for which it is defined- all x except 1. That reduces to f(x)= x for

**those**values of x- x not equal to 1.

A simpler example of that is (x- 1)/(x^2- 1)= (x- 1)/((x- 1)(x+ 1))= 1/(x+ 1) for all x**except**1. The left side is not defined for x= 1 but the right side is so they are not equal for x= 1. - Mar 29th 2012, 03:25 PMskeeterRe: f functions and domain/range
graph of f[f(x)] ... note the discontinuity at x = 1