Question

Let f : R → R be a continuous function satisfying f(x) = x + ∫ f(t) dt ,x∈ [0,x] for all x ∈ R. Then the number of elements in the set S = {x ∈ R ; f(x) = 0} is- 

(A) 1 

(B) 2 

(C) 3 

(D) 4 

Answer 1

Correct Option :- (A) 1

Explanation :-

f ′ (x) = 1 + f(x) ⇒ f(x) = e^x – 1 

f (x) = 0 ⇒ ex = 1 x = 0 One solution