Consider the function f(x) =x+1/x-1 ; x ≠ 1 1. fof(2) = ____ (a) 1 (b) 2 (c) 3

Question

Consider the function f(x) =\(\frac{x+1}{x-1}\); x ≠ 1

1. fof(2) = ____

(a) 1

(b) 2

(c) 3

(d) 4

2. What is the inverse of f?

3. f(3) + f^-1(3)

Answer 1

1. fof(2): (b) 2

2. Let g : range of f → R- {1} inverse of f Let ‘y be any arbitrary element in the range of f
then y = f(x) = \(\frac{x+1}{x-1}\)

⇒ xy – y = x + 1 ⇒ x(y – 1) = y +1

Let us define g : range of f → R- {1} as

3. f(3) = 2, f^-1(3) = 2

f(3) + f^-1(3) = 2 + 2 = 4.