Consider the following functions. (x) = x, f,(x) = x², 1,(x) = 3x - 7x² g(x) = c,f,(x) + Cf2(x) + czf3(x) Solve for c,, c2, and c3 so that g(x) = 0 on the interval (-o, 0). If a nontrivial solution exists, state it. (If only the trivial solution exists, enter the trivial solution (0, 0, 0}.) {c, C2, C3} = {| Determine whether f, f, fz are linearly independent on the interval (-o, o). linearly dependent O linearly independent

Q: Given f(x) = 4x + 3 and g(x)= 2x – 1, find f(x) – g(x). О 4х — 1 O 4x -2 O 2x + 4 O 6x О бх +2

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Q: Use the method of undetermined coefficients to find a particular solution of the constant…

A: In this question, we will find the Particular solution of the differential equations.

Q: If f(x) = (x + 6)² then f(x + h) – f(x) = Ax + Bh + C h Find the constants A, B, and C. A= B= and C=

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Q: If h ( x ) = 3 x 2 − 2 x, then find h (5).

A: Let there is a function fx to find the value fa we need to substitute x=a in the expression.…

Q: Find the particular solution of the function defined by the following properties: f"(x) = 1&x; f'(1)…

A: Given: f''(x) = 18x,  f'(1) = 5,  f(3) = 80 To find: The function f(x) from the given options.

Q: If f(1) = 4 and f(n) = f(n – 1) + 3 then find the value of f (4).

A: Given f(1)=4, f(n)=f(n-1)+3

Q: Find f (x) for f(x)=-- O f-¹(x) = -5x2 O = f-¹(x) 2 5x+3 O f-¹(x)= 3x 2 O f-¹(x) = 5x-3 -2x 5x-3…

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Q: if f(x)+g(x)= 3x +2 and g(x) = x - 1 then f(x)= %3D а. 2х+3 O b. 3x+2 О с. 3х-2 O d. x+4

A: Given,f(x)+g(x)=3x+2g(x)=x-1f(x)=?

Q: Given the functions f (x) = 3x - x.g(x) =7,h(x) = 9z, find gof(z) O gof(x) = 3-7 O gof (x) = () (322…

A: Composite function is a function in which there are more than one function and value of one function…

Q: Which of the following functions are 1-to-1? f(x) = x² + 2x 3, g(x) = 4x – 1, h(x) = |2x +2| %3D

A: Only  g(x) is one to one function.... Concept: If the derivative of given function is strictly…

Q: If F(x) = x2 - 3x + C and F(-1) = 4, what is the value of C?

A: Given: Fx=x2-3x+C  and F-1=4

Q: Find (g o f)(x) and (fo g)(x) for the given functions f and g. x) - o(x) = Vx-2 x- 2 (go n(x) - (fo…

A: Given: fx=1x2, gx=x-2 To Find: gofxfogx

Q: Solve f(x) = 0, where f(x) = (x + 4)²(1 - x).

A: We have been given the function  f(x)=(x+4)2(1-x)

Q: Two balloons, one red and one green are released from a platform at t=0. Each balloon goes up for a…

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Q: Anna and Bob are the only residents of a small town. The town currently funds its fire department…

A: Ans:

Q: f(0)=2 and f(n+1)=3f(n)-1. Find f(4)

A: To find f (4), obtain f (0), f (1) and f (2) as follows.

Q: 2. If f(x)=((-4,4)(-3,0)(-2,8)(-1,-2)(0,-4) (1,5)) and g(x)=((-3,0)(-1,6)(1,-4) (3,-2)), determine…

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Q: . Let f(x) = x2 + x + 3, g(x) = 5x + 3 and h(x) = 2x2 – 4x + 1. Find the following: a. f(4x) b.…

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Q: h(x)= 3x+5 j(x)=-2, I-3 What is h(x)/j(x)? What is the domain?

A:

Q: 2. How many, and what type, of solutions exist for the function f(x) = x - 3x- 27x + 19x² +114x-72?

A: Given: f(x)=x5-3x4-27x3+19x2+114x-72

Q: 2. Find f(g(5)) if f(x) = 2z + 5 and g(x) = 3x2 %3D O f(g(5)) = 675 O f(g(5)) = 155 %3D O f(g(5)) =…

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Q: If f(x) = 2x - 4, find f-¹(x). OX-4 2 O-2x+4 O X+4 2 O 4-x 2

A: The inverse of a function f is a function that undoes the operation of f.

Q: If f(x) = 2x +2, g(x) = - 3x - 2x-2, and h(x) = 7x² +5, find f( - 3). f(- 3) =O (Simplify your…

A: Given: fx=2x+2, gx=-3x2-2x-2, hx=7x2+5 For finding value of f-3, we put x=-3 in given fx and…

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.