engineering recuitment AAI ATC Junior Executive 2025 Mock Test Series Mathematics Differential Calculus Applications of Derivatives
Let f(x) be a fucntion such that f(x + y) = \(\frac{f(x)+f(y)}{1+f(x)f(y)}\) ∀ x, y ∈ R and f '(0) =1. Also - 1 < f(x) < 1 ∀ x ∈ R. Then f(x) is increasing in the interval:
1
( - ∞, - 1) ⋃ (- 1, 0)
2
( - ∞, - 1) ⋃ (- 1, 0) ⋃ (0, 1)
3
( - ∞, - 1) ⋃ (- 1, 0) ⋃ (0, 1) ⋃ (1, ∞)
4
( - ∞, ∞)