True/False: If ƒ is entire and |f(z)| > 2 for all z E C with |2| > 1, then f is a constant function.

Q: For all functions f and g, f o g(x) = go f (x). O True O False

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Q: f is a function of all real numbers defined by f(x)=x2, what is f-1({x |0<x<1})?

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Q: (b) Let the function f: R → R defined by 3x for x > 3 2x2 + 3 for - 2 < x< 3 3 x? – 7 for x<-2 f(x)…

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Q: Let f be the function defined above, where k is a constant. f(x) = x²+kx-2 3x²+4x+3 x³ + 2 0 2e 2-e…

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Q: Let ƒ(x) = 2x2 + 5x and g(x) = 4x + 1. Find g[f(x)]

A: Given: fx=2x2+5x . gx=4x+1 . gfx can be calculated by replacing the x by fx in the function gx as,…

Q: Consider the function f(x) = 12x5 +30x4 - 160x³ + 7. - f(x) has inflection points at (reading from…

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Q: (p²+1)² ; P € C\ {+i, -i}

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Q: Consider the function f (x) = 3 – |x – 4|| a. Graph the function and verify that f(1) = f(7) b. Note…

A: The given function is f(x)=3-x-4 The function can be redefined as  f(x)=x-1,      x&lt;47-x,…

Q: Let C be the contour (blue) given in the figure below and let f(z) be any function with If (z)| <…

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Q: of Əf Find and дх ду Əf дх — II for the following function. f(x,y) = (5x – 2y)5

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Q: Show if the following functions are concave or convex. f(x₁, x₂) = -x-x₁x₂ - 2x²; S = R² f(x1, x2,…

A: Given :  fx1,x2=-x12-x1x2-2x22fx1,x2,x3=-x12-x22-2x32+0.5x1x2 To check that functions are concave or…

Q: Consider the following functions: f1(x) = sin(x1) cos(x2), æ € R² f2(x, y) = x'y, x, y E R" f3(x) =…

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Q: If f is an even function, then f −1 exists.

A: Consider an even function ,f(x)=x2 For,x=±2,we have f(±2)=4 Hence, given function is not…

Q: Let C be the contour (blue) given in the figure below and let f(z) be any function with If(2)| <v2.…

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Q: Let f be a function defined as follows: f(x) = 2.3-2 if x 3. if x > 3. x-3 What type of…

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Q: Find the value of b such that the function f is continuous everywhere. ƒ(x) = b |5-x| x² - 7x + 10…

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Q: Find the intervals on which the graph of f is concave upward. f(x) = In (x² – 2x + 10)

A: f(x)= In(x2 - 2x + 10) To find the intervals on which the graph of f is concave upward.

Q: Determine whether Rolle's Theorem applies to the following functions on the given interval. If so,…

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Q: Explain the Pythagoras theorem with its proof and applications. Use citation in APA format, commas,…

A: claim- explain the pythagoras theorem with its proof and applications statement- In a right angled…

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

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: