Question

Which function has an inverse function?

/=means the _ of a fraction like 4
_
5
F(X)= [x+3]/5

F(X)=X^5-3

F(X)=X^4/7 +27

F(X)=1/x^2

Answer 1

F(X)=X^4/7 +27 .......

Answer 2

The correct option is 2.

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,

`f(x)=\fracx+3}{5}`

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,

`F(x)=x^5-3`

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,

`F(x)=(x^4)/(7)+27`

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,

`F(x)=(1)/(x^2)`

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.