Question

Let a function f : A → B is defined as f(x) = x²/(x² + 1). If f is onto function, then find the set of values of A ∩ B.

Answer 1

Clearly, domain of a function is R.

i.e. D_f = A = R.

Now, range of the function is [0, 1)

Thus, R_f = [0, 1).

Since f is onto function, so R_f = B.

Thus, B = [0, 1)

Hence, A ∩ B = [0, 1).