Math miscellaneousHard
Question
If f(x + y) = f(x)f(y) ∀ x, y ∈ R and f(0) ≠ 0 and F(x) = 
, then 
F(x) dx - 
F(x)dx is equal to -
, then F(x) dx - F(x)dx is equal to - Options
A.
F(x)dx
F(x)dxB.0
C.F(x)dx
F(x)dxD.
F(x)dx
F(x)dxSolution
f(x + y) = f(x)f(y) ⇒ f(x) = ax;
F(x) =
⇒ F(x) = F(-x)
∴
F(x)dx - 
f(x) dx - 
f(x)dx = 
f(x)dx
F(x) =
⇒ F(x) = F(-x)∴
F(x)dx - f(x) dx - f(x)dx = f(x)dxCreate a free account to view solution
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