In Problems 1 through 6, show directly that the given functions are linearly dependent on the real line. That is, find a non- trivial linear combination of the given functions that vanishes identically. 1. f(x) = 2x, g(x) = 3x², h(x) = 5x – 8x² 2. f(x) = 5, g(x) = 2 – 3x², h(x) = 10 + 15x2 3. f(x) = 0, g(x) = sin x, h(x) = e* 4. f(x) = 17, g(x) = 2 sin² x, h(x) = 3 cos? x 5. f(x) = 17, g(x) = cos² x, h(x) = cos 2x 6. f(x) = e*, g(x) = cosh x, h(x) = sinh x %3D %3D

Q: Show that the equation f(x) =x+3x-1%=Ø %3D has at least one solution,

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Q: If f(x)=−x and g(x)=−x, then f and g have identical graphs.

A: The objective of this question is to determine whether the graphs of the functions f(x) = -x and…

Q: A) To the nearest inch, estimate the height of the maple tree in 2011.  inches B) Use the equation…

A: y = 9.44x + 84.182

Q: If F(x) = (x − 1) 2 + 1; Evaluate F′(−1), F′(0), F′(2)

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Q: Consider the functions, h(x) = 3x – 7 and k(x) = . b. Find h(k(x)) X+7 | a. Find h(k(- 2)) c. Find…

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Q: 6.Given f(x)= 3x – 2 and g(x)= x2 – 5x, find f(-1)+g(2)

A: The given functions are: fx=3x-2 and gx=x2-5x To find f-1 replace x with -1 in fx=3x-2 and similarly…

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: f(x)=(3x+1)1/2; a=5; b=16.081/2

A: It is given that fx=3x+1. We have to compute the linearization of the function fx at the point a=5.…

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: Consider the differential equation (1– v2)y' – ytanx = yv²tanx Which of the following is the linear…

A: Given(1-2) y1 - y tan x = y2 tan x —(I)(1-2) y2- y1 - y1-2 tan x = tan x —(II)Put       y1-2 = u…

Q: 3. Given f(x) = -7x-8-4sin(8)- 3e-6x – 4n² then determine the defining equation of f(x).

A: To determine the defining equation of f(x) from f'(x), we integrate f'(x) with respect to x.

Q: If the point (1,4) lies on the graph of y = f(x), then the y-coordinate of the corresponding point…

A: Given that (1, 4) lies on the graph y = f(x)  Therefore f(1)= 4  Transformations of this graph is y…

Q: Find the fixed points of the following functions: (a)         f(z) = 4z3   (b)           g(z) =…

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Q: Given the functions            g(x) =   5x - 2      find g-1(x)…

A: The given function is gx=5x-24x+3. Replace x by y and gx by x and then solve for y as follows.

Q: function is given such that f(4)−f(6)=9. If the function is linear, which of the following could the…

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Q: If f(z) is a linear function, f(- 3) = - 5, and f(4) = 0, find an equation for f(x) %3D %3D f(2) -

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Q: Please find the integral f dr.

A: Introduction

Q: 1))Write the equation of a linear function: a) with a slope of 2/3 passing through (6, -1) b)…

A: To write: The equation of linear function  (a) with a slope of 23  and passing through (6, -1) (b)…

Q: Experiments indicate the braking distance, d, before a car comes to rest from a speed, v (Table 2).…

A: 1st we will make linear equations for a,b and c   and then will use cramer's rule to find values of…

Q: If f(x)=−x and g(x)=−x, then f and g have identical graphs.

A: The objective of the question is to determine whether the graphs of the functions f(x) = -x and g(x)…

Q: 4. If f is a coordinate system on a line /, determine whether or not each of the following functions…

A: We need to determine whether each will be a coordinate system or not.

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: Let f(x)f(x) be the height of a maple tree in inches and xx the number of years since 2000. A linear…

A: A) The linear mode is fx=9.44x+84.182. The estimated height of the maple tree in 2011(= 11 years)…