The number of points where g(x) = max {f(x), 6, 7 - |x|} is nondifferentiable ∀ x ∈ [-10, 10] are

Question

Let a function f(x) satisfies the condition f(x+ y) = (f(x) + f(y))/f(x) such that f(0) = 2 and f(x) ≥ 0.

The number of points where g(x) = max {f(x), 6, 7 - |x|} is nondifferentiable ∀ x ∈ [-10, 10] are 

(A) 5 

(B) 6 

(C) 7 

(D) 8

Answer 1

Answer is (A) 5

See Fig.

Hence, the number of points is 5.