Understanding Domains and Ranges for Inverse Functions - A Noob's Guide

[elemis]

Supposing I have a function f(x).

Let us suppose that f^-1(x) has the same equation as f(x).

Will the domain and range as defined for f(x) be the same as for the inverse ?

 

[Tinyboss]

In general, if f-1 is the inverse of f, then the domain of f is the range of f-1, and vice-versa. So your question becomes, "if f has the same equation as its inverse, then does its range have to be the same as its domain?" The answer to that is "no". Consider f(x)=-x, and try restricting the domain of f to some subset of the real numbers.

 

[elemis]

In general, if f-1 is the inverse of f, then the domain of f is the range of f-1, and vice-versa. So your question becomes, "if f has the same equation as its inverse, then does its range have to be the same as its domain?" The answer to that is "no". Consider f(x)=-x, and try restricting the domain of f to some subset of the real numbers.

No, you misunderstood the question I posed.

Lets us say that the range for f(x) is f(x) > 3 and its domain is x>0

Now let's say f^-1(x) has the same equation as f(x).

Will f^-1(x) have the same range and domain as f(x) ? That is, will the domain be x>0 and the range f^-1(x)>3 ?

 

[disregardthat]

Will f^-1(x) have the same range and domain as f(x) ? That is, will the domain be x>0 and the range f^-1(x)>3 ?

Tinyboss understood you perfectly, and gave a counterexample.