Let f be a differentiable function with f(0) = 1 and / f'(1) dt = x². Then Of(x) = COS X Of(x) = (x+ 1)e* Of(x) = x + 1 Of(x) = x² + 1 None of these

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A: The figure given is

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A: Please refer to the image below

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Q: Let f and g be functions satisfying that f(1) = 3, g(1) = 4, f'(1) = 1, g'(1) = 5. For the following…

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A: f'x=x2-4

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Q: assume f(g(x))=x and f'(x)=1+f2(x) for all x. show that g'(x)=1/(1+x2)

A: Differentiate both sides of f(g(x))=x with respect to x. Use chain rule on the left side.