Looking for any function that satisfies this criterion.

I'm thinking that the question asks for the definition of any function f(x) such that f(x) = n when x = n! (including an appropriate domain restriction, too).

In other words, does the function f(x) = x! have an inverse?
 
Since the domain is not specified, I feel it is up to the answerer to give it. I feel Jeff's solution is just fine. The function !:N->N is one-to-one. However, I would be inclined to say there is no inverse.
 
mmm4444bot said:
I'm thinking that the question asks for the definition of any function f(x) such that f(x) = n when x = n! (including an appropriate domain restriction, too).

In other words, does the function f(x) = x! have an inverse?
Click to expand...

Yes, thank you. I wasn't too clear in my original post. Exactly what you have said for all \(\displaystyle x>1\) so that all \(\displaystyle f(x)\) has only one output per input.

Basically, does \(\displaystyle f(x) = x!\) have an inverse for \(\displaystyle x>1\)?
 
You must log in or register to reply here.
Top