Let f : R → R be a continuous function satisfying f(x) = x + ∫ f(t

1.	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» Correct Option :- (A) 1 Explanation :- f ′ (x) = 1 + f(x) ⇒ f(x) = e^x – 1 f (x) = 0 ⇒ ex = 1 x = 0 One solution

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»

Correct Option :- (A) 1

Explanation :-

f ′ (x) = 1 + f(x) ⇒ f(x) = e^x – 1

f (x) = 0 ⇒ ex = 1 x = 0 One solution

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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

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