Let f: &reals; → &reals; be defined by f(x) = x2- (x2/1+x2) for all x ∈ &reals;. Then

Question

Let f: &reals; → &reals; be defined by f(x) = x2- (x2/1+x2) for all x ∈ &reals;. Then (A) f is one - one but not onto mapping (B) f is onto but not one - one mapping (C) f is both one - one and onto (D) f is neither one - one nor onto

Tardigrade Admin · Accepted Answer

f(-x) = f(x), so many-one and into as Codomain is R

Q. Let f : ℝ → ℝ be defined by f(x) =x2−1+x2x2​ for all x ∈ ℝ. Then

f is one - one but not onto mapping

f is onto but not one - one mapping

f is both one - one and onto

f is neither one - one nor onto

f(-x) = f(x), so many-one and into as Codomain is R

Q. Let f : ℝ $\to$ ℝ be defined by f(x) $= x^{2 -} \frac{x ^{2}}{1 + x ^{2}}$ for all x $\in$ ℝ. Then