Suppose that for all real x S'(x) = -g(x) and g'(x) = f(x). (a) Show that f²(x)+g²(x)= C for some constant C. (b) Suppose that f(0) = 0 and g(0) = 1. What is C? (c) Give an example of a pair of functions that satisfy parts (a) and (b).

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A: Inverse of function problem....

Q: he first principle to determine f'(x) of the following functions: f(x)=x2 f(x)=x2-

A: f(x) = x2 ddx(f) = f'(x) = 2x

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A: We are given f(x)=9x+8 and g(x)=x+9 and we need to find different composition of the function.

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Q: Find f'(x) and simplify. f(x)= x x+2 Which of the following shows the correct application of the…

A: F′(x)=(x+2)22​Explanation:If you have any questions let me know in comment box thankyou for your…

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A: Here we need to plot two functions such that and f''(0) is undefined.In other words f(x) is concave…

Q: 1 x-2 f(x)=- y g(x)=√x

A: To find the composite function

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A: Step 1:Step 2:

Q: Determine whether the functionf is one-to-one by examining the sign of f' (x). (a)ƒ(x) = x³ + 9x2 –…

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Q: On which interval is the function f(x) = x2 - 2x - 8 decreasing? A [-2, 4] B (-∞, 4) C…

A: Given, f(x) = x2 - 2x - 8

Q: Suppose that for two functions f &amp; g, we know the following information:f(8) = 16f'(8) = 6f(3) =…

A: The given composition function is

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Q: A function f is defined, for x<, by f(x) = 2x² – 6x + 5. (i) Express f(x) in the form a(x – b)² +c,…

A: Please see the below picture for detailed solution.

Q: Find the general form of f if f'(x)= 9f(x). f(x) = ]

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Q: Let F(x) = f(f(x)) and G(x) = (F(x))² and suppose that f(9) = 13, f(13) = 3, f'(13)=9, f'(9) = 7…

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Q: For the function f(z) 2(x – 5) + 7, which of these equations describes f '(r), the inverse of the…

A: We wil use concept of inverse function to find the answer.

Q: Let f'(x)= = (x-1) (x-2)(x+1) and g'(x) = (x+2)(x-3) (x+3)

A: We have to find the interval in which f(x) and g(x) are decreasing.

Q: 5. Sketch the graph of one function f(x) that has all of the following properties: a.) f(-2) 0 b.)…

A: As per our guidelines we are supposed to answer  only one question. Here question 5) answer.

Q: f(x) |f'(x) | g(x)| g'(x) -4 8 5 -3 10 4 00 3. 3.

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Q: Express the function in the form fog. (i) F(x) = (2r + r*)ª. (ii) F(r) = %3D 1+ VE

A: Answer

Q: Can f(z) = | Re (z2) | + i.Im (-z) be derived from the function z=0? Show it.

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Q: Find a function f so that f '(x) = 3x + 2x + 5 and f(1) = 10.

A: Given, f'(x)=3x2+2x+5 To find the function f, Integrate f'(x) with respect to x  we get,…

Q: Determine whether the functionf is one-to-one by examining the sign of f' (x). (a)ƒ(x) = x³ + 9x² –…

A: first we look at the sign derivative if  f'x&gt;0 or  f'(x)&lt;0   for all x in their domainthen…

Q: For f(x)=1/1-x, find f(f(x)) and f(f(f(x))) (show work)

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