For the following statements, state if the are true or false. If they are true, prove them. If they are false, give a counter example. (a) Suppose that f: R R is an injective differentiable function. Then f is either increasing or decreasing. (b) Suppose that f: RR satisfies f(x)| ≤ x². Then f'(0) exists.

Q: 3)Verify Rolle's Theorem for the function f (x) = 2x² + 3 defined over the interval -5, 5]. Justify…

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A: See the attachment

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A: Which of the  following must be there for a function than is  concave up everywhere .

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A: Use the definition of composite function f∘gx=fgx, to obtain f∘fx. fx=2x+3x-2f∘fx=ffx=f2x+3x-2

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A: first we analysis to given question that how to find f, G, h then we compute F(x) function.

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A: It is given that;  H(x)=x2+1 and; (f∘g)(x)=H(x)

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Q: Examine whether the following function is Analytic or not f(z) = [z]²

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