# Domain of an inverse function

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

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Defennder
Homework Helper
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.

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

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

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

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

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