If (f +g) € R[a, b] , then (f.9) € R(a, b] (f - 9) € R[a, b] E R[a, b] none of these

Q: Let 1 f(x) = 2 9, - 2 < x < 5 - The domain of ƒ¯'is the interval [A, B| where A = and B =

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Q: f(x,y)=x+y f(x,y)=x-y

A: Solution Given f(x,y)=x+yf(x,y)=x-y we need to draw the following function

Q: Let h(x)=f(x)g(x). If f(8)=4,f′(8)=−1,g(8)=5, and g′(8)=−3, what is h′(8)? Do not include "h′(8)="…

A: We have to find value of h\'(8) where information is given below:

Q: Find the order of the one-step method Un+1 = Un +5f(un +5f(Un))+ (f (Un) + f(un + hf(uUn))) 2 2 4…

A: We are given an one-step method and we have to find its order. To do that we will use limits and…

Q: 3. Determine whether the statement is true of false. If it is false, give an example that shows it…

A: Given: f'(x)=g'(x) So, we can write as: dfxdx=dgxdxdfx=dgx...Integrate on both…

Q: (-2, 7.333) 10 (0, 0) (5.058, 0) (-3,558, 0) 10 (3, -13.5) Complete the following statements. f'(x)…

A: The graph of the function fx is To complete the following statements :

Q: (a) Suppose f is a function and f(4) = 2. Is it possible that there exists another value c for which…

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Q: -5 -20 -10 9- Which ordered pairs are included in f(x)? Included in f(x) Not included in f(x) 2.

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Q: Let k(x)=f(x)g(x)h(x). If f(−2)=−5,f′(−2)=9,g(−2)=−7,g′(−2)=8,h(−2)=3, and h′(−2)=−10 what is…

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Q: Suppose that f  has domain A and  g has domain B .(a) What is the domain of  f+g?(b) What is the…

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Q: 4- If f is R-I, then |f| is R-I and |S f| < SIFI (H.W)

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Given the relationA={(4,3), (6,4), (7,3), (8,5)}. Which of the following statement is TRUE? (A Only…

A: A relation is function if each input has a unique output⇒each x value gives only one y…

Q: 4. If F(x) = f(xf (xf(x))), determine F'(1) when f(1) = 2, ƒ (2) = 3, f'(1) = 4, f'(2) = 5, f'(3) =…

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Q: The domain of f(x) = V x2 + x – 6 | is : a) ]-4, 1[ b) ]-00, 4[U]1, +0[ c) ]-00,-3[U]2, +00이 d) ]-3,…

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Q: 18. What can you deduce about the sets X and Y if you know, a. there is an injective function f: X…

A: Given that two sets X and Y.a)There is an injective function

Q: For f(x) = Vx+5 and g(x) = x + 8, the domain of х-9 x is? (0, 0) Option 1 [-5, 9) U (9, 0) Option 2…

A: Let's find.

Q: Q#4, A function f : Z x Z -> Z is defined as f(m, n) = 3n - 4m. Is this function injective,…

A: A function f: ⥮ X ⥮ → ⥯ is defined by f(m,n)=3n-4mInjective:  f(0,0) = 0f(4,3) = 3(4)-4(3) =…

Q: Let F=x y z+A +x'y z'+x'y'z'+x y'z. Suppose simplified form is F=x'z'+x y +x z, What is A =? x' y z…

A: Let us go back from the reverse. That is from the simplified form…

Q: 67. If F(x) =f(g(x)), where f(-2) = 8, f'(-2) = 4, f'(5) = 3, g(5) = -2, and g'(5) = 6, find F'(5).…

A: F(x) = f(g(x))   x | f (x) | f ' (x) | g (x) | g ' (x) -------------------------------------- -2 | 8…

Q: A = {5,6} B = {5, 7 ,8} S = {n | n >= 3 is an odd integer} A relation R from AxB to S is defined…

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Q: A = {a, b, c}, B = {7,12, 13, 17, 30} f is a injective function from A to B. If f(a) = 17 and f(b) =…

A: The solution are next step

Q: Determine whether the statement is true or false. If f(1) > 0 and f(5) < 0, then there exists a…

A: Given f(1)&gt;0 and f(5)&lt;0

Q: Let f= {(2,6) (3,8) (4,5) and g(x)=3x+5 f(3)-g(3)

A: It is given that  f= {(2,6) (3,8) (4,5)} From the above x value, determine the g(x). g(2)=3*2+5=11…

Q: Let f(x, y, z) = In + y (a) Evaluate f(3,-4, 9). (b) Find the domain ofF (Enter your answers as a…

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Q: Which among the choices have the operation on function that is equivalent to I+ 12 O f(z) = + 2z -…

A: Recall: fgx=f(x)g(x)

Q: 3. If f(x) = 4, what is the value of x given that f(x) = 2x+1 A. 2 В. 32 C. 1/2 D. 4 4. Find f(x-1)…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Let h(x)=f(x)/g(x), where f(−3)=7,f′(−3)=−9,g(−3)=−2, and g′(−3)=1. What is h′(−3)? Do not include…

A: h(x) = f(x) / g(x)Hence, h'(x) =[g(x)f'(x) - f(x).g'(x)] / [g(x)]2

Q: 3. Let f : A → B. Then 1gf = f and f14 = f. Hint. You may use the fact that fg, for functions f, g,…

A: Let               f1 : X→Y , f2 : X→Y be two functions, then we say that the functions f1 and f2 are…

Q: If F(x) = f(g(x)), where f(-5) = 9, f'(-= 7, f'(4) = 2, g(4) = -5, and g'(4) = 4, find F'(4). %3D…

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Q: If h(x) = (f.g)(x) and f(2) = 5, f'(2) = 3, g(2) = 1, g'(2) = -1 Then h' (2) = -20 - 7 – 2 - 6

A: Given  h(x) =(f.g)(x) And f(2)=5,f'(2)=3 g(2)=1,g'(2)=-1

Q: Find  ƒx( x, y, z) , ƒy ( x, y, z) , ƒz ( x, y, z) , and ƒyz ( x, y, z)  for the following.

A: The given function is fx, y, z=lnx2-5xz2+y4. This implies that,

Q: 2. If g(x)=√√3-x and f(x) = x³ +1 evaluate the following: gof(-1) b. (g-f)(2)

A: Given, g(x)=3-xf(x)=x3+1

Q: 4. If f(x)= and g(x)=determine the domain of g(f(x))?

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Q: Suppose that f(5) = 1, f'(5) = 6, g(5) = –3, g'(5) = 2. Using appropriate rule, fin (fg)'(5) b.…

A: Solution-  Given f(5)=1, f'(5) =6, g(5)= -3, g'(5)=2 a) (fg)'(5) we use product rule of derivative…

Q: What is the domain of if x0 Give the range of f(x) = x< 0 A. (-00, 00) B. (-4, 0) C. (-4, 00) D.…

A: As per guidelines we have to solve three suboarts Since ist two question answer is not in option  So…

Q: Given the function f:{1,2,3} → N defined by f = {(1,3), (2,5), (3,1)} Is f1-1 Is fonto What is the…

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Q: if f(x,x2) =,0 < x, < 1,0 < x2 < 1, then f(x2/x,) = 1

A: Let X and Y be two continuous random variable with joint density function f(x,y). The marginal…

Q: Evaluate (f− g) , (1) and (3f + 2g) , (1), assuming that f , (1) = 3 and g , (1) = 5.

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Q: 8. What is the domain and range of the following relation? y=x−2x−3 y 14 X --6-5-4 a) {x E R}, {y…

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Q: D = {[x, f(x)]: (-1, 2), (0, 1), (1, 2), (2, 5), (3, 10)} Write the rule for f(x). x + 1 2x x² + 1

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Q: 2 if f) = k x?,-1<x<1,then k = true false

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Q: if G-H-F such that and H-F <R-k So...... R-k =G-H

A: Draw a diagram representing this scenario. Use the diagram to deduce a conclusion.

Q: 5- If f is R-I, then f is R-I (H.W)

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Q: Which of the following is the set required for F2[x]? 35 - a) {1, (x + 1), (x + 1)²} b) {0, x, x2}…

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Q: Let h(x)=f(x)/g(x), where f(−3)=7,f′(−3)=−9,g(−3)=−2, and g′(−3)=1. What is h′(−3)?

A: Given query is to find indicated derivative.

Q: Estimate f(1.02, 2.02) given that f(1, 2) = -5, f-(1, 2) = 5 and fy(1, 2) = -3. f(1.02, 2.02) -

A: Here is the solution of the given problem.

Q: If f = {(1, 4), (-2, 0), (3, 0.5), (p, 0)} and g = {(1, 1), (-2, 2), (0.5, 0)}, find each of…

A: Given g = {(1, 1), (-2, 2), (0.5, 0)},

Q: (a) y=-f Be B.

A: Please see the below picture for detailed solution.

Q: f(1) = 4 ; f(2) =-1; f(3)=-3 Relation: f(n+1) = 5 [f(n)]-2 f(n-1) Given: c. f(5) D. f(-1)

A: Given that f1=4, f2=-1 ,f3=-3Relation : fn+1=5fn2-2fn-1Solution :put…

Q: Let f be the function from {a, b, c, d} to (1, 2, 3, 4} with f (a) = 4, f (b) = 2, f (c) = 1, and f…

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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.