The function that has an inverse function is:
We know that " A inverse of a function f(x) exist if it is both 1-1 and onto "
We know that the modulus function is not 1-1.
Since, there are two different 'x' such that the function have the same value.
and take x= 7
In both the cases we have: f(x)=4
Hence, the function does not has a inverse.
We know that a polynomial with even degree is not 1-1.
As it is symmetric about a line x=a
Hence, option: B is incorrect.
Again it is a polynomial of even degree.
Hence, it does not has a inverse.
As the function is both 1-1 and onto.
Hence, the function has a inverse and the inverse function is calculated as:
Hence, the inverse function is:
The answer is:
1. You have the following function given in the problem:
2. You can rewrite it as below:
3. Then, you must apply interchange the variables:
4. Now, you have:
5. When you apply ln you obtain:
6. Now, clear y: