Continuous Functions f(x) Satisfying f(x)>1 and f(x) = x + ∫f(t)dt for All x

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Find all continuous functions f(x) satisfying
f(x)>1 and f(x) = x +(1 to x integral) \int f(t).dt
for all x
 
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Do you mean

f(x) = x + \int_{1}^{x} f(t) dt

?
 
Hint: Show that f(x) has to be differentiable. Then differentiate both sides of the equation.
 
owlpride said:
Hint: Show that f(x) has to be differentiable. Then differentiate both sides of the equation.

So i did it but how can i provide the result by this way
 
owlpride said:
Do you mean

f(x) = x + \int_{1}^{x} f(t) dt

?

Yes i mean this integral
 

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