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2 years ago

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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