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stellarik [79]
2 years ago
5

Plz help!!!

Mathematics
2 answers:
Harman [31]2 years ago
7 0

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

so B is correct!

Sholpan [36]2 years ago
4 0

Answer:  The correct option is

(B) f^{-1}(x)=\dfrac{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)=\dfrac{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)=\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}.

Thus, the required inverse of the given function is

f^{-1}(x)=\dfrac{1}{x-1}.

Option (B) is CORRECT.

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