Problem 4. Consider the function µ: N→Z defined as follows: u(1) =1 and if n 2 2, then S(-1), ifn P1... P, uhere the Pi are distinct; H(n) = otherwise. For instance, u(15) = 1, µ(3) = -1, and u(18) = 0. (1) Is the function u completely multiplicative? If yes, prove this, otherwise show that it is not by exhibiting an example. (2) Is the function u multiplicative? If yes, prove this, otherwise show that it is not by exhibiting an example.

Q: 3. Consider the function f(x) = (g(x) – h(x)) and the following function values: g(2) = 5 h(2) = 4…

A: We have to find derivative

Q: 10. Given the functions f(r) = ² – 3 and g(z)= Vr, find the following. a) (fog)(r) b) (go)(z)

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Q: differentiable and

A:

Q: 6. Give four non-trivial functions f(x), g(x), h(x) and j(x) such that Vx2 – 1+5 - (f ogohoj)(x) = V…

A:

Q: 2. Consider the following function: y = f(x) = x" – 14x® (a) Determine in which regions this…

A: A function is increasing or decreasing that is determine by    f'(x)>0 or f'(x)<0 A function…

Q: 12. The following is a graph of y = f(t): 6 -5- -4 -3- 2 -2 -1 2 5 6 -1- -2 Let g(x) = | f(t) dt and…

A: We have to solve the problem

Q: 5. Find the inverse function of f(x) = 3x - 7. 3.2.1) mont noita ovitostjd a (ewors diw) Jou Maitsa…

A:

Q: 2. Consider the following function: y = f(x) = x" – 14° (a) Determine in which regions this function…

A:

Q: 3. k= For what value(s) of k will the domain of the function m(x): = x-8 be equal to (-∞, 9) U…

A:

Q: f(z) = z2

A: We have to show the given function is not analytic at any point.

Q: 3. SOIve the y' = e(2x - 4), y(5) = 0. Then, compute y(5.25). Remark. In this problem, we can easily…

A:

Q: find three functions, h(x), g(x) and f(xr) so that K(x) is the composition of h, g, and f, in other…

A: We will use the concept of composition of functions.

Q: Find the function f(x) such that f'(x) = f(x)(1 – f(x)) and f(0) = (Use f for f(x) in your…

A:

Q: Today's outside temperature is modeled by the function T = Q(t), where T is measured in degrees…

A: Today's outside temperature is modeled by the function T=Qt,where T is measured in degrees Celsius…

Q: If y is a function of x such that y'>0 and y">0 for all x. Which of the following could be part of…

A: Given,        It is given that y'> 0 for all x and       y''>0 for all x.

Q: 1.9. Consider the CES technology f(x1,x2) = [a₁x² + a₂x2]. Show that we can always write this in the…

A: To show that it can write the CES technology function in the form f(x1,x2)=A(ρ)[bx1ρ+(1−b)x2ρ]1/ρ,…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.