Question

Which function has an inverse function?

In this picture, there are the options, which one it's?
A, B, C or D
Will give you 15pts

Answer 1

well, it is one that, when reflected across the y=x line, is still a function (use vertical line test)

the first one will not be a function when reflected
2nd won't either
3rd won't
4th will

D is answer

Answer 2

The function whose inverse is also a function is:

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

Explanation:

The inverse of a given function f(x) is also a function if the function is one and one.

a)

`f(x)=(|x+3|)/(5)`

As we know that the modulus function is not one-one.

Hence, the inverse of this function is not a function.

b)

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

We know that a odd-degree polynomial is always one-one.

Hence, the inverse of this function is also a function.

c)

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

The even degree polynomial is not a one-one function.

Hence, it's inverse is not a function.

d)

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

We know that the graph of this function is not one-one and hence it's inverse is not a function.