Question

Function f: R → R, defined by f(x) = `x/(x^2 + 1)` ∀ x ∈ R is not

Options

• one-one

• onto

• Neither one-one nor onto

• None of the above

Answer 1

Neither one-one nor onto

Explanation:

For, x₁, x₂ ∈R, consider

`f(x_1) = f(x_2) ⇒ x_1/(x_1^2 + 1) = x_2/(x_2^2 + 1)`

⇒ `x_1x_2^2 + x_1 = x_2x_1^2 + x_2`

⇒ `x_1x_2 (x_2 - x_1) = x_2 - x_1`

⇒ `x_1 = x_2` or `x_1x_2` = 1