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Let f: R rarr R be a continous function ...

Let `f: R rarr R` be a continous function satisfying `f(x) = x + int_(0)^(x) f(t) dt`, for all `x in R`. Then the numbr of elements in the set `S = {x in R: f (x) = 0}` is -

A

1

B

2

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
A
`f'(x) = 1 + f(x) rArr f(x) = e^(x) - 1`
`f(x) = 0 rArr e^(x) = 1 , x = 0` One solution
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KVPY PREVIOUS YEAR-KVPY-exercise
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