# Domain of an inverse function

1. Jun 5, 2008

### nokia8650

The function f is defined by f(x) = ln(4 - 2x), x<2, and x is a real number

write down the domain of the inverse.
I know that the domain of the inverse is the range of the function, but I am puzzled as to what that would be! Would it just be any real number?

Thanks

Last edited: Jun 5, 2008
2. Jun 5, 2008

### Defennder

The range of the natural logarithm is -infinity to infinity. That means to say that that would be the range of that function if the range of 4-2x where x<2 is also just any real number. What is the range of 4-2x where x<2?

EDIT: I just realised that the range of 4-2x where x<2 is restricted to positive real numbers.

Last edited: Jun 5, 2008
3. Jun 5, 2008

### nokia8650

The range of 4-2x would be greater than 0.

4. Jun 5, 2008

### nokia8650

Hi, thanks, but im still confused! What would be the range of the function then?

5. Jun 5, 2008

### Defennder

That would be the range of the natural logarithm, as stated earlier. Do you see why?

6. Jun 5, 2008

### nokia8650

So the range would be any real number? Yes, i see why; it is a logarithm of any number >0, as 4-2x > 0.

Last edited: Jun 5, 2008