3.3.4. Suppose that f and g are different constant functions from S to S. Show that ƒ og + gof. Proof. Since f and g are different constant functions, there exists distinct elements ES and E S such that f(x) = and g(x) : x € S. Then (ƒ o g)(x) = for and (gof)(x) = for x E S. This implies fog + gof.

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Q: Suppose that T(0) = a and T(1) = b are some constants. Define the running pairwise average as, for n…

A: Given: Tn+2=12Tn+1+Tn for n≥0 T0=a T1=b To find: The limit of Tn as n→∞.

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Q: 6. Suppose t > 0. Consider the functions f(x) = e* and g(x) = xt. Show that ext for all x > 0, if…

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Q: For what values of a and b will f(x) be continuous on everywhere at x = 2 if the function is x² – 4…

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Q: Quest The moment generating function of X is given by Mx() = exp(2e - 2} and that of Y by Myt) = (e…

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Q: 1.2.10 1 if x < a, f (x) = 2a elsewhere on (-T,"|, where 0 < a < T. Sketch for two different choices…

A: Since, you have post multiple question here. I am answering first one. Please post again with…

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Q: 4. Find the branch points of the following functions and indicate a suitable cutting. a. fi(z) =…

A: (a) Consider the given function as, f1z=2z2+1

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Q: 4. Suppose the following functions are a general solution of: y(4) + a3y/" + azy" + a;y' + a0y = 0

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Q: 9. 6) Suppose that g is continuous and that g(x) dx = 2 and g(x) dx = 16. Find g(x) dx.

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Q: Provide what is asked for in each item. 3x (9 – x2) (9 – 3x?)2 54.x(x² + 9) (9 – 3x2)³ * 1. Given…

A: Given:  fx=x39-3x2f'x=3x29-x29-3x22f''x=54xx2+99-3x23 To Find:  a To find the domain of f and the…

Q: 4. Let 2; x + f(x) = 1; x = Prove that f is R. I. on [0, 1] and find G f(x)dx. Hint: See a similar…

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Q: If f'(x) = x(x – 5)(x + 1)*, then f(x) has a local minimum at: Select one: а. X = 0 only O b. x = 5…

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Q: A consumer has preferences described by utility function u(x1,x2)=In(1+x1)+x2. Suppose p1=1, p2=3,…

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Q: Determine the interval(s) on which the function is continuous: 2r+ 7 212-3x-9 if x 1/2 Ox1/2 Ox1/2…

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Q: 20 Use this graph of y = f(x) and the fact that 3 5 6 1 10 il i2 i: -2+ to compute the following: L…

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Q: The following table shows values of a periodic function f(x). The maximum value attained by the…

A: Note that the function is defined only for multiples of 6.

Q: 1. Suppose G(x) is an antiderivative of g(x) and F(x) is an antiderivative of f(x). If f(x) = g(x),…

A: Antiderivative

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A: Given    g(1) = −4 g'(x) =x2+15

Q: 9- The general solution for the PDE (DD, + D,D-12D =0 is a. u(x, y) = G,(x)+G,(x+y)+G,(x-y) b. u(x,…

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A: The given function is f(x,y)=arccos(x2+y2-3)+ln(x2+y2-3) It can be rewritten as…

Q: If f:R→R is a continuous even function, then | F(x)dx is necessarily equal to -5 O10 O Cannot be…

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Q: = 1 – 3, h(x) = VT, then If f(x) = x* + 6, g(x) fogo h(z)-

A: Find your answer below

Q: 1. Suppose that 0 is an estimator for a parameter 0 and E(0) að + b, for some nonzero constants and…

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Q: 4.1.5. Let f(x,y) = (x² – y², 2xy). Show that Df(a,b) (h, k) = (2ah– 2bk, 2bh+ 2ak) for all (a, b) e…

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Q: 6.Suppose that the joint p.m. f. of X and Y is X- 00 Yə -1- 09 10 Determine: (1)-The value of a;…

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A: Domain: The domain of a function is set of all values for which is well defined. Given:

Q: 2. Let G = Z,xZ4, and find [G:H] for: a) H = {0}xZ4. %3D

A: We have to find [G:H]

Q: Suppose there is no known formula for g(x), but we know that g(2) = -1 and d (z) = V2 +5 for all x.…

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Q: f(x) = x3-3x2+3x-1 ;   m = -1   ;  [-1, 2]

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: A clamped cubic spline S that approximates a function f on [1,3] is defined by : (2 + ²/(x-1) + a(x…

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Q: Given x2 if x 2 f(x) – f(2) a) Determine the left and right limit of the function b) For what…

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Q: Compute the following values for the given function. h(s, t) = 2s ln(t) − 7t ln(s) h(1, e) =…

A: a) Given that s=1 and t=e  Then we plug the values in the formula and simplify

Q: 9) The Wronskian of the functions f(x) = -5, g(æ) = 7x² y h(x) = e3 is given by a) W(f(x), g(x),…

A: The details calculation is given below

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A: If a  function f(x) is defined on an interval [a,b] and it's second derivative exists at x=c, then…

Q: Suppose that T(0) = a and T(1) = b and are some constants. Define the running pairwise average as,…

A: The function of T is determined using the given recurrence relation as shown below.

Q: (a) Use the Chain rule to compute the derivative of g(x) = (1+x²)® [ set g(x) = h(k(x)) where h(z) =…

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Q: Suppose that we don't have a formula for g(x) but we know that g(1) = -4 and g'(x) = V x2 + 15 for…

A: g(1)=-4, g'(x)=x2+15 Finding the value of g '(1) g '(1)=12+15=1+15=16=4

Q: For which of the following functions and domains does the Extreme Value Theorem guarantee the…

A: Check which function guarantee maximum and minimum value on the domain using extreme value theorem

Q: If ø(x) =(x)+ f(1-x) and f"(x)<0 for all x e increasing in [0,1/2] and decreasing in (1/2,1].…

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Q: 9. Suppose that N(h) is an approximation to M for every h > 0 and that M = N (h) + K,h+ K,h? + K3h…

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Q: 3. If f(x) = -x, g(x) = 2x + 1 and h(x) = x2, find fogoh 1 point %3D %3D О А. х2 - 1 О в. 2х2 - 1 О…

A: We use fogoh=f(g(h(x))).

Q: Solve the following linear independent and Wronskian. 2. Are the functions y, = e* and y2 = x…

A: Here we have to determine whether the given functions are linearly independent.  We have,  y1=ex…