Question

Let the function g : (-∞, ∞) → (- π/2, π/2) be given by g(u) = 2tan-1(eu) - π/2. Then, g is

(A) even and is strictly increasing in (0, ∞)

(B) odd and is strictly decreasing in (−∞, ∞)

(C) odd and is strictly increasing in (−∞, ∞)

(D) neither even nor odd, but is strictly increasing in (−∞, ∞)

Answer 1

Answer is (C) odd and is strictly increasing in (−∞, ∞)

We have

Therefore, g(4) is strictly increasing function.