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

In summary, the function f is defined as ln(4 - 2x) with a domain of x<2 and a range of -infinity to infinity. The domain of the inverse would be the range of the function, which is restricted to positive real numbers. Therefore, the range of the inverse would be any real number greater than 0.
  • #1
nokia8650
218
0
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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  • #2
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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  • #3
The range of 4-2x would be greater than 0.
 
  • #4
Hi, thanks, but I am still confused! What would be the range of the function then?
 
  • #5
That would be the range of the natural logarithm, as stated earlier. Do you see why?
 
  • #6
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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FAQ: What is the domain of the inverse function for f(x) = ln(4 - 2x)?

What is the domain of an inverse function?

The domain of an inverse function is the set of all possible input values for which the inverse function is defined. It is the range of the original function.

How do you find the domain of an inverse function?

To find the domain of an inverse function, you can switch the x and y values and solve for y. The resulting equation will be the inverse function, and the domain will be the set of all possible x values for which the inverse function is defined.

Can the domain of an inverse function be different from the domain of the original function?

Yes, the domain of an inverse function can be different from the domain of the original function. This is because the inverse function is essentially a reflection of the original function over the line y=x, which can result in different input values being defined.

Can an inverse function have a limited domain?

Yes, an inverse function can have a limited domain. This means that there may be certain input values for which the inverse function is not defined.

What happens if the original function has a domain of all real numbers?

If the original function has a domain of all real numbers, then the inverse function will also have a domain of all real numbers. This is because the inverse function will also be defined for all possible input values.

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