Question

Select the correct answer from given alternatives.

Let the function f be defined by f(x) = `(2x + 1)/(1 - 3x)` then f^–1 (x) is ______.

विकल्प

• `(x - 1)/(3x + 2)`

• `(x + 1)/(3x - 2)`

• `(2x + 1)/(1 - 3x)`

• `(3x + 2)/(x - 1)`

Answer 1

Let the function f be defined by f(x) = `(2x + 1)/(1 - 3x)` then f^–1 (x) is `underline((x - 1)/(3x + 2))`.

Explanation:

f(x) = `(2x + 1)/(1 - 3x)` = y say. Then

2x + 1 = y (1 – 3x)\

∴ y – 1 = x (2 + 3y)

∴ x = `("y" - 1)/(2 + 3"y")` = f^-1 (y)

∴ f^-1 (x) = `("x" - 1)/(2 + 3"x")`