Consider the following functions. f₁(x) = x₁ f₂(x) = x², f3(x) = 2x - 3x² g(x) = c₁f₁(x) + C₂f₂(x) + C3f3(x) Solve for C₁, C₂, and c3 so that g(x) = 0 on the interval (-∞, ∞). If a nontrivial solution exists, state it. (If only the trivial solution exists, enter the trivial solution {0, 0, 0}.) {C₁, C₂, C3} = Determine whether f₁, f₂, f3 are linearly independent on the interval (-∞, ∞). O linearly dependent O linearly independent

Q: F f(x) = x2 - 9 & g(x) = 2x- 5 then find the solution for (fog)x) <0 %3D

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Q: B.Give the maximum and minimum points of the functions on the interval I. (a) f(z)=x – 2 ;I=[-1,1]…

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Q: Consider the function f(x) = ax + b, where a and b are constants. Which of the following is one of…

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Q: Consider the following functions. f1(x) = 0, f2(x) = x, f3(x) = ex g(x) = c1f1(x) + c2f2(x) +…

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Q: Find a function f(x) so that h(x) = (gof)(x) given that -2x³ – 6x² 6x² + 5x+1 and g(x): = h(x) =…

A: (g∘f)(x) = g(f(x))

Q: = Solvex (t) = Ax(t) where A 3 -2 [1] [8] = 4 and (0)

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Q: f(x)=4x+3    Evalute and simplfy the following (round to 2 decimal places if necessary)…

A: Given,            fx=4x+3To find : Evalute and simplfy the following                 fx+h-fxh

Q: Match each of the following conditions with an equation. f(x) = 24x - 4 fil(0) f(0) = f(0) = 0 = y =…

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Q: 1. Determine if the following functions are continous at the interval I (a) f(x) = x – 1; I=[-2,2]…

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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)=3x-²-5x¯³+1 and g(x)=√√x, then derivative of (gof)(x) is: a. b. C. 1/1/23 1 2 3x ² 5x 3 1 d.…

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Q: A homogeneous second-order linear differential equation, two functions y₁ and y₂, and a pair of…

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Q: f₁(x) = x₁ f₂(x) = x², f3(x) = 4x - 2x² g(x) = C₁f₁(x) + C₂f₂(x) + c3f3(x) olve for C₁, C₂, and c3…

A: f1(x)=x, f2(x)=x2, f3(x)=4x-2x2g(x)=c1f1(x)+c2f2(x)+c3f3(x) we have to solve for g(x)=0

Q: If ​f(x)=−3x5+x3−6x2+9​, then ​f(x)→enter your response here as x→−∞​, and ​f(x)→enter your…

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Q: 8. Let f(x) = -x-2, g(x) = 4x + 1, h(x) = 2(x − 3) +1 (a) Evaluate h(-2) (b) Evaluate f(0) (c) Solve…

A: Since you have posted multiple sub-parts in the question, as per guidelines, we are supposed to…

Q: If f(x) = and g(x) = 2x, then the solution set of (fog)(x) = (go f)(x) is Select one: Oa. O a. O b.…

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Q: X f(x) = {x² + 2x 1 at a = 0 if x = 0 if x = 0

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

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Q: With f(x) = 3x +1 and h(x) = 2x – 4, find (f o h)(5)

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Q: Consider the following functions. f₁(x) = x, F₂(x) = x1, f3(x) = x + 7 g(x) = c₁f₁(x) + c₂f₂(x) +…

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Q: Determine at what point(s) the graphs of f(x) = /2r+6 and g(z) = vAz – 8 intersect. Let f(z) = (10r…

A: Let us consider, To find point of intersection, solve these two equations: