contestada

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

Respuesta :

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

so B is correct!

Answer:  The correct option is

(B) [tex]f^{-1}(x)=\dfrac{1}{x-1}.[/tex]

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

[tex]f(x)=\dfrac{x+1}{x}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

Let y denotes f(x). Then,

[tex]y=f(x)~~~~~~\Rightarrow x=f^{-1}(y).[/tex]

Substituting this value in equation (i), we get

[tex]f(x)=\dfrac{x+1}{x}\\\\\\\Rightarrow y=\dfrac{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)=\dfrac{1}{y-1}\\\\\Rightarrow f^{-1}(x)=\dfrac{1}{x-1}.[/tex]

Thus, the required inverse of the given function is

[tex]f^{-1}(x)=\dfrac{1}{x-1}.[/tex]

Option (B) is CORRECT.