Let g be continuous on [a, b] where g(x) > 0 for all x € [a, b] and define F(t) = f g(x)dx for te [a, b]. Show that if f is continuous, then [far = [ fdF f f(x)g(x)dx.

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A: The given statement : f-1(A ∪ B) = f-1(A) ∪ f-1(B) is true and we shall prove this statement.

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A: Introduction ∫-∞∞fxdx=1 The total area under the curve fx of pdf is 1.

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Q: continuous function h(x),

A: Differential equation

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A: We can explain this statement by 2 explainations given below

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A: The solution is below.

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