5.|x-y|=||x|-|y||| iff y=x for all x,yeX and for some >> 0 6. If x0 and (y) bounded, then (x80

Q: 45. Let g(x) = [x]. Find a) g-¹({0}). c) g-¹({x|0<x< 1}). b) g-¹({-1, 0, 1)).

A:

Q: Suppose X and Y are r.v.s such that E(X) = 4, Var(X) = 48, E(Y ) = 2, andVar(Y ) = 5. Find upper and…

A: To find the upper and lower bounds for E(XY), we need to use the Cauchy-Schwarz inequality. For any…

Q: 5. Let f(x)=3x² and necessary. a. f(g(x)) = x-9 g(x)= -,x-1, x+1 find the following. State domain…

A: Solution is uploaded below.

Q: Suppose that ƒ′(x)&lt;= 1 for 1&lt;= x&lt;= 4. Show that ƒ(4) - ƒ(1)&lt;=3.

A: Show that:

Q: 19. The interval for function |(3 )/2 z-1|<2 is -2/3 ,21 (- 2/3 ,2) (-2/3 ,2] - 2/3 ,2)

A:

Q: 7. 3+x 7 3-x Find f(x) such that h(x) = (fo g)(x) and g(x) = 3+x h(x) = 3-x ,7 f(x) = D

A: It is given that gx=3+x73-x7,hx=3+x73-x79

Q: . Let G(x)= x+3)2, if x ≤ -1; 2-x if 1<<1; Find all values of a where G is not continuous. , if x 1.

A:

Q: 2 2. Is f(x) = { = { x²-1 x+1 if x = -1 if x −1 continuous at x = −1? (Show your work using limits.)

A: See this solution in below.

Q: (1) If x + 0, then +0 and A = x. (2) Let a, b e R. a² + b² = 0 if and only if a = 0 and b = 0. %3D…

A: Note: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts…

Q: 5. The function f(x) is defined as: 4x3 +17x2 + 13x +36 x -4 ontinuous for all values of x. What…

A: solution:-f(x)=4x3+17x2+13x+36x+4     x&lt;-45x2+2x+a                       x≥-4f(x) is continuous…

Q: 9. For what value of the constants A and B is the function A√x+6-1 for Br² +2 f(x) = 2 Ar + B f…

A:

Q: 9. The interval for function (6-x)/4< (3x-4)/2 is

A: Find your answer below

Q: 3. Determine the x interval(s) on which the function is increasing.

A: From the given Figure, it is observed that the graph of function has local maximum at x=-4  and…

Q: 6. Let f(x) be defined as follows: f(x) = {2f x is an integer (1 if x is not an integer Find each of…

A:

Q: 1. Graph f(x) = 3-* over the interval [-2, 2] y. 7 -8- -7+ 6+ -5-

A: The given function is:f(x)=3-x

Q: Here R^3 - {(0,0,0)}. please proof this using submersion. thank you.

A: Given: R3=(0,0,0) To find: The set M=(x,y,z)∈R3:x2+2y2+z2=4xyz a submanifold of R3.

Q: 4. x- 1 < |x - 2|

A: "As per our guidelines we are allowed to solve only first complete question kindly repost others."…

Q: 6. For each of the following, is it a well-defined function? Explain. (a) (b) (d) a: R→Z a(x) = B(n)…

A:

Q: 10. Let f(z) = 4z7z²+3z +1 and g(z) = 4z7. Show that f(z) - g(z)| < |g(z)| for |z| = 1.

A:

Q: 2. f(x)= Domain: f(-2)= (2x+1 x≥1 x²+3 Function: Yes No Continuous: Yes No f(6)= f(1) = x <1 Range:

A:

Q: 43. Show that f(x) = x4 - 7x² - 8x - 3 has exactly one cal point c in the interval (2, 3).

A:

Q: 4. x t +5 and y = 5-t for 1<t = %3D t

A: We are asked to find the domain of the graph.

Q: 3. (a) Find a unit in Z[√2] which is not equal to 1 or -1. Hint: Use 1 (b). (b) (*) Show that Z[√2]…

A: The objective of the question is two-fold. First, we need to find a unit in the ring Z[sqrt(2)] that…

Q: 00 ak 10. If f(x) = ar(x - 3)* for all real r, then the function F(r) = (-3)*+1 has %3D k=0 k+ 1 k=0…

A:

Q: 3. For f(x) = 15x²-3 16x²+9x+8 As x → ∞, y → || As x →∞, y →

A:

Q: 7. On the graph below, indicate an interval (xo -8,xo +8) so that 0<x-xo<6 guarantees f(x)-L<8.…

A: Introduction: Calculus's "epsilon-delta" concept of a limit is an algebraically exact way to express…

Q: -4 if x1

A: The given function is: f(x)=-4        if  x&lt;-2(x+1)2-1    if  -2≤x≤1-14x+2if  x&gt;1

Q: 3. Let r = (4, –3, 1, –5) € R'. Which of the following equals ||r||? (a) 5 (b) 13 (c) V51 (d) v63

A:

Q: 1. v₁ = (4, −2, 6, −4), V₂ = (6, −3, 9, −6)

A:

Q: 3. Please help!!: Calculate the domain of the function

A: If you have any questions let me know in comment box thankyou for your question.