Question

Plz help!!!

Select the correct answer.
What is the inverse of the function f(x)=x+1/x?
A.)F^-1(x)=x/x+1
B.)F^-1(x)=1/x-1
C.)F^-1(x)=x-1/x+1
D.)F^-1(x)=x/x-1

Answer 1

we know that f(1)=2 so f^-1(2)=1

so B is correct!

Answer 2

Answer: The correct option is

(B)
`f^(-1)(x)=(1)/(x-1).`

Step-by-step explanation: We are given to select the correct expression that is the inverse of the following function :

`f(x)=(x+1)/(x)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

Let y denotes f(x). Then,

`y=f(x)~~~~~~\Rightarrow x=f^(-1)(y).`

Substituting this value in equation (i), we get

`f(x)=(x+1)/(x)\\\\\\\Rightarrow y=(f^(-1)(y)+1)/(f^(-1)(y))\\\\\\\Rightarrow yf^(-1)(y)=f^(-1)(y)+1\\\\\Rightarrow yf^(-1)(y)-f^(-1)(y)=1\\\\\Rightarrow (y-1)f^(-1)(y)=1\\\\\Rightarrow f^(-1)(y)=(1)/(y-1)\\\\\Rightarrow f^(-1)(x)=(1)/(x-1).`

Thus, the required inverse of the given function is

`f^(-1)(x)=(1)/(x-1).`

Option (B) is CORRECT.