What is the domain of the inverse function for f(x) = ln(4 - 2x)?

[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

 

[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 realized that the range of 4-2x where x<2 is restricted to positive real numbers.

 

[nokia8650]

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

 

[nokia8650]

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

 

[Defennder]

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

 

[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.