Question

Let f: `R - {1/2}→R - {1/2}, f(x) = (x - 2)/(2x - 1)` be a function such that x = m is the solution of f(x) + 2f^–1(x) + 2 = f(f(x)), then m is equal to ______.

विकल्प

• 0.00

• 1.00

• 2.00

• 3.00

Answer 1

Let f: `R - {1/2}→R - {1/2}, f(x) = (x - 2)/(2x - 1)` be a function such that x = m is the solution of f(x) + 2f^–1(x) + 2 = f(f(x)), then m is equal to 2.00.

Explanation:

f^–1(x) = `(x - 2)/(2x - 1)`

⇒ f(x) = f^–1(x)

⇒ f(f(x)) = x

⇒ f(x) + 2f^–1(x) + 2 = f(f(x)) reduces to `3/(2x - 1)` = 1

3 = 2x –1

2x = 4

⇒ x = 2