Answer:
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,
[tex]f(x)=\frac{|x+3}}{5}[/tex]
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,
[tex]F(x)=x^5-3[/tex]
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,
[tex]F(x)=\frac{x^4}{7}+27[/tex]
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,
[tex]F(x)=\frac{1}{x^2}[/tex]
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.
