Question

A function f:R – {– 1} → R – {1} is defined as f(x) = x/(x + 1). prove that f is onto function.

Answer 1

Now, let y = x/(x + 1)

⇒ yx + y = x

⇒ x(y - 1) = - y

⇒ x = - y/(y - 1)

Then the range of a function is R – {1}

Thus, R_f = R – {1} = Co-domain

Hence, f is onto function