? ? ? ? Determine which of the following pairs of functions are linearly independent. 1. f(x) = x³, g(x) = |x|³ 2. f(t) = 3t² + 21t, g(t) = 3t² - 21t 3. f(x) = x², g(x) = 4|x|² 4. f(x) = e³x, g(x) = ³(x-3)

Q: Find the domain of the following function 1 f (x) = 2 + f (x) Vx

A: Given function,                            f(x)=12+x

Q: 5. f(x) =-2 x-1 6. f(x) = 2 7. f(x) = x² + 3

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Q: Differentiate the following functions. 1. f(x) = x* +5-2 +x -2 +4x4 2. F(t) = (t - 2t + 1)(2t2 + 3t)

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Q: 8. Find f-1 (x) for f (x) = 2-4

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Q: 1. How to define the function, f(x, y) = 15x+4x*y+15y 3x+3y to make it a continues function?

A: We have to find the given function is continuous.

Q: Evaluate the following functions. 1. Iff(x) = x? - 2x +7, find a) f(0), b) f(2y+1). 2. If F(y) = vty…

A: Given:1. fx=x2-2x+72. Fy=yy-32

Q: 1. Given the function S(a) = Find (a) all the a and y-intercepts,

A: The solution is given below in the next step: Also in step 3 graph is provided for better…

Q: 4. Evaluate the functionf(x) = x² + 1 and g(x) = x - 4. Find a. (fᵒg)(3) b. (gᵒf)(1)

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Q: Consider the following initial value problem: [3, 0≤t≤2 10, t>2 y" + 25y = y(0) = 6, y'(0) = 0 Using…

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Q: If f is the linear function f = 3x - 1, what is the value of ? dx

A: Given: f(x)=3x-1 To find out: df/dx

Q: 1.Solve the following polynomial equations.  a)  2X3+1=x2+2X

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Q: 1. A quadratic function is defined by f(x) = 2x + 6x - 20. Which of the following expresses f(x) as…

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Q: If f(x) = 2 + 3x – 4x², determine the value of the dependent variable f(5) – f(3). Show your work.

A: We can solve the problem by putting the value 5 and 3 in the given function.

Q: 4.2 Find the solution subject to the following boundary and initial conditions of the heat equation,…

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Q: linearization

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Q: L Matching Type. Match the functions in Column A with their corresponding derivatives in Column B.…

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Q: dont understand the fourth and fifth row of equation of gh(x) and why the function is invalid?

A: Solution