Let f be a differentiable function on R and satisfying f(x)=-(x^2-x+1) e^x+ ∫_0^x e^x-y· f^'(y) d...

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Let f be a differentiable function on R and satisfying the integral equation x ∫_0^x f(t) d t-∫_0... Let f be a differentiable function on R and satisfying the integral equation x ∫_0^x f(t) d t-∫_0...
If f(x) be a differentiable function satisfying f(y) f(x/y)=f(x) ∀ x, y ∈ R, y ≠ 0 and f(1) ≠ 0, ... If f(x) be a differentiable function satisfying f(y) f(x/y)=f(x) ∀ x, y ∈ R, y ≠ 0 and f(1) ≠ 0, ...
The function f(x)=e^x+x, being differentiable and one-one, has a differentiable inverse f^-1(x). ... The function f(x)=e^x+x, being differentiable and one-one, has a differentiable inverse f^-1(x). ...
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