The correct option is 2.
Step-by-step explanation:
A function has an inverse function if and only if it is a one-to-one function. It means for each value of x there exist a unique value of y.
In option 1,
It is an absolute function. For each value of x there axis more than 1 value of f(x). Therefore this function does not has an inverse function.
In option 2,
The degree of the function is 5 which is an odd number. Therefore it is a one-to-one function. Therefore this function has an inverse function.
In option 3,
The degree of the function is 4 which is an even number. Therefore it is not a one-to-one function. Therefore this function does not has an inverse function.
In option 4,
The degree of the function is 2 which is an even number. Therefore it is not a one-to-one function. Therefore this function does not has an inverse function.
Hence option 2 is correct.