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

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The function f(x) = ln(4 - 2x) is defined for x < 2, which restricts the input values. The range of the expression 4 - 2x, given this domain, is limited to positive real numbers. Consequently, the range of the function f(x) is all real numbers since the natural logarithm can take any positive input. Therefore, the domain of the inverse function is also all real numbers. The discussion clarifies that the inverse function's domain corresponds to the range of f(x).
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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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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.
 
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The range of 4-2x would be greater than 0.
 
Hi, thanks, but I am still confused! What would be the range of the function then?
 
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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