The logistic function given by f(r) = is a sigmoid (s-shaped) function useful in many 2. 1+e- areas of mathematics and computer science. The function f is a bijection, whose domain is R and range is (0, 1). Given an arbitrary interval (a, b), by using the composition of f with an appropriate function g : (0, 1) → (a, b), show that R| = |(a, b)|.

Q: Define functions f: {0,1,2} → R+ and g: R+R by f(x) = 4x and g(x) = log2 (x). Write down the ordered…

A:

Q: A function f has the form f(x) = a + b In(x). Find f if it is known that f(1) = 8 and f(2) = 12.…

A:

Q: Define f(x) = 2 – 3x? What is the domain of this function? (-00, 2) (-00, 2] [-3, 0) (-x0, 0) [0, 0)

A:

Q: A function f has the form f(x) = a + b In(x). Find fif it is known that f(1) = 1 and f(2) = 8.…

A: Find your answer below

Q: The linearization of f (x) = x² based at 3 is L (x) = [ Select ] [ Select ] (x - [ Select ] Done […

A:

Q: Determine whether the given set of functions is linearly independent on the interval (-o, ∞). f1(x)…

A: The solution is given as

Q: Determine whether the pair of functions is linearly independent or linearly dependent on the real…

A:

Q: h(x) = (f °gXx) Let h(x)=(2x-5) and f(x) =x, find g(x). 1. Let h(x) = Vx-5 and f(x)= Vx, find g(x)…

A:

Q: find functions f and g so that f ∘ g = H.

A: given: Hx=1-x2 we have to find the functions f and g so that f ∘ g = H.

Q: determine the value of the parameter a that will make the function f(x) = [ax+1, x- -1

A: The given function is fx=ax+1,    x<-1x2-3,     x>-1 To find: Value of parameter a

Q: Use a computer algebra system to compute f(k)(x) for k = 1, 2, 3 for the following functions: (a)…

A: given,        a.  f(x) = cot(x2)b.  x3+1

Q: Consider the function f : RH→ R defined by f(x) = 2e(2z+5) log(2r+5) + If f convex or concave ? Why…

A:

Q: f(t) dt, where fis the function whose graph is shown. Jo Let g(x)=

A:

Q: Determine whether the given set of functions is linearly independent on the interval (-00, 00⁰).…

A:

Q: find functions f and g so that f ∘ g = H.

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

Q: Find  f ∘ g ∘ h. f(x) = 1/x ,  g(x) = x3,   h(x) = x + 4

A:

Q: 2 Let f(x)=Vx and g(x)=- x-4

A: Given that  f(x)=√x and g(x)=2/(x-4) To find the f of g

Q: Find a function f(1) such that | f(z)dr= 2² – 5.

A:

Q: Let two functions be f(x) = x2 - 4 and g(x) = (fo g)(x)? What is (fo g)(x) -4 %3D x2 +8x+16 (fo…

A: Given:fx=x2-4   and gx=1x+4f∘gx=?

Q: 7. Find the explicit particular solution to the initial value problem. Hint: Linear DE. у 3 cos (x)…

A:

Q: Let ƒ(x) = x/x - 2. Find a function y = g(x) so that (ƒ ∘ g)(x) = x.

A:

Q: A function f has the form f(x) = Aekx. Find f if it is known that f(0) = 140 and f(1) = 266. (Hint:…

A:

Q: Compute f(5) (e) forthe function f(x) = x³.In(x+)

A: f(x)=x3.ln(x4)f(x)=4x3ln(x)Differentiatef'(x)=4x2+3x2ln(x)f'(x)=4x2+12x2ln(x)Differentiatef''(x)=8x+…

Q: Let Σa," converges at z=3+4i. Then radius of convergence of the power n=0 series Σα=" is, n=0 (a) ≤5…

A: Result: Suppose a power series ∑anzn with an,z∈C converges for some single point z0 in complex…

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.