Select the correct answer which function has an inverse function?

The function that has an inverse function is:

            D.  

Step-by-step explanation:

We know that " A inverse of a function f(x) exist if it is both 1-1 and onto "

A)

We know that the modulus function is not 1-1.

Since, there are two different 'x' such that the function have the same value.

Take x=1

and take x= 7

In both the cases we have: f(x)=4

Hence, the function does not has a inverse.

B)

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.

C)

Again it is a polynomial of even degree.

Hence, it does not has  a inverse.

D)

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:

               Option: D

To solve this problem you must follow the proccedure shown below:

 1. You have the following function given in the problem:

  f(x)=50000(0.8)^x

 2. You can rewrite it as below:

 y=50000(0.8)^x

 3. Then, you must apply interchange the variables:

 x=50000(0.8)^y

 4. Now, you have:

 x/50000=(0.8)^y

 5. When you apply ln you obtain:

 ln(x/50000)=ln(0.8)^y
 ln(x)-ln(50000)=yln(0.8)

 6. Now, clear y:

 y=[ln(x)-ln(50000)]/ln(0.8)