f(x) = 2x, g(x) = 3x², h(x) = 5x – 8x²

Q: Verify that g'(x) 1 where g(x) = v2x – 3. %3D V2r – 3

A: Giveng(x)=2x-3.To verify g'(x)=12x-3  is the derivative of g(x).

Q: Show directly that the given functions are linearly dependent on the real line. That​ is, find a…

A:

Q: State the equation of f(x) if D = {x = R] x * f(x) f(x) f(x) f(x) = = = 2x+1 3x - 2 x + 1 3x + 2…

A: Topic = Functions

Q: Express ax + bx + c as a linear combination of the functions f(x) = 3, g(x) = 4x, and h(x) = -x²,…

A:

Q: Determine whether there exists a constant c such that the line x + cy = 1: passes through (3, 1).

A: We have to determine the value of constant c such that the line x+cy=1 is passing through the point…

Q: 2) Find the fixed point of the functions : A. f(x) = x² + 5x + 3 B. f(x) = x³ – 4x² + 6x – 2 C. f(x)…

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Q: Express ax2 + bx + c as a linear combination of the functions f(x) = 5, g(x) = 4x, and h(x) = -x²,…

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Q: Find the linear approximation to the following function at the given point a. ƒ(x) = e3x - 6; a = 2

A: Given,f(x) = e3x-6at a = 2

Q: Consider the quadratic function f(x) = ax2 + bx + c, a ≠ 0. If a > 0, then f has aminimum that…

A: f(x) = ax2 + bx + c f'(x)=2ax+b f"(x)=2a   To find the critical value we solve f'(x)=0

Q: If f (x) is a linear function, f (1) = 0, and f (2) = 1, what is f (3)?

A: fx is a linear function such that f1=0 & f2=1

Q: Show that if f and g are linear, then so is f + g. Is the same true of fg?

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Q: Show that a cubic function f (x) = x3 + ax2 + bx + c is increasing on (−∞,∞) if b > a2/3.

A: Given function is: fx=x3+ax2+bx+c Then we get, f'x=3x2+2ax+b

Q: find a formula for the linear function f(x) that satisfies f(5)=7 and f(0)=-3

A: Given information:f(5)=7 and f(0)=-3

Q: Find h(0), h(x + 3), and h(-x) for h(x) = x + Vx² – 1. 2)

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Q: Consider f(x)=ax3+bx2+cx+d Under what conditions on a,b,c,and d does the graph of a cubic function…

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Q: Find the zero(s) of f. Ay -1 2 x f(x) = -2x2 + 3x %3D 2.

A: The function is given by  To evaluate : The zeros of the function fx

Q: Show that the real-valued function f: R → R defined by f(x) = x° x E R. 3x2 + 3x + 1 increases for…

A: Answer

Q: A quadratic function is defined by f (x) = x +5x - 24. Which of the following expresses f (x) as the…

A: Factorizing the given quadratic function

Q: Find the derivative of the function?

A:

Q: Let f and g be linear functions with equations f(x) = m1x + b1 and  g(x ) = m2x +b2. Is f ° g also a…

A: The given linear functions are fx=m1x+b1    and  gx=m2x+b2. This implies that,…

Q: Show directly that the given functions are linearly dependent on the real line. That is, find a…

A: Given function is  f(x)=6xg(x)=5x2h(x)=9x-12x2 Definition: If n functions f1,f2,f3,...fn are said to…

Q: If f(x) = x2 – 5x + 7, what are the co – ordinates of the minimum of y = f(x – 2)?

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Q: Let F = Z, [x] (x³ + 3x + 2) and α=x+ (x+3x+. (x³+3x+2) €F. Find a³.

A:

Q: Which is equal to () (x) given that g(x) = 1 – 3x and h(x) = Vx? %3D Vx – 3xVx 3xVx Option 1 Option…

A: Let's find.

Q: Give two distinct linear functions ƒ and g that satisfy ƒ'(x) = g'(x); that is, the lines have equal…

A: It is given that fx and gx two distinct function.

Q: The domain of the function /1- a² – y² ln(a² + y2 – 1) is empty. True False

A: We have to check

Q: if f(z) = (ax – x³ + 3xy²)+ (by – 3x² y + y) is analytic, then the value of a and is

A:

Q: the Wronskian of the set of functions: 3x² - 1, x⁴ - 2, 2x⁵ + 3 is equal to 4x³ (9x⁵ - 10x³ + 90x +…

A: In the given question,    It is given that wronskian of  {3 x2 -1, x4 -2 , 2x5 +3}  is { 4x3 (9x5…

Q: The domain of the function f(x,y) = In(2 – /x2 + y² ) is: %3D - x² +y² < 4

A: The explanation of the solution as follows:

Q: Show directly that the given functions are linearly dependent on the real line. That is, find a…

A: Use the given information.

Q: Consider the quadratic function f: R3 →R defined by f(X) = xỉ – x1x2 + x – x2x3 + x3 + 1 A: Express…

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Q: Find the linearization at x = a. g(x) = 20x² x - 3 a = 12

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Q: If f:R R* is a polynomial function satisfying the functional equation f{f(x)} = 6x - f(z), then…

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Q: Show that f is linear of slope m if and only iff(x + h) - f(x) = mh (for all x and h)

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Q: 12. If f(x) is a non-constant linear fucntion and g(x) is a quadratic function, then what type of…

A: f(x) is linear function so f(x) can be expressed as  f(x)=ax+b, where a≠0 and b are constants. g(x)…

Q: Find the linear approximation to the following functions at the given point a. ƒ(x) = 4x2 + x; a = 1

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Q: f(x) = x^4 + x^3 – 6x^2 – 5x – 15, use the reminder theorem to evalute a, f(5)    b, f(-3)

A:

Q: If f(x) = 3x – 1, h(x) = 6x + 5, and fog=h, find g(x). %3D

A:

Q: If f(x)=1/5x^5-3/4x^4-4/3x^3+60, then what is the set of x values for which f has a relative…

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Q: The function f(x) = 2x³ – 27x2 + 48x – 3 has two critical numbers. - The smaller one is x = and the…

A: We have to find critical numbers for the function: fx=2x3-27x2+48x-3 We know that critical points of…

Q: The linear function f(x) = ax + b is a constant function if?

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Q: Show that the three functions: f₁(x) = ex-8f₂(x) = exf3(x) = 4(2x-2) are linearly dependent.

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Q: Find the linearization at x = a. 1 f(x) = = 5 +3

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Q: Suppose z is a function of r and y, and x² + y² + z² = xe² + ye² + ze³. Solve əz əz for and əx ду

A: Topic = Derivative

Q: Suppose z is a function of x and y, and z^xe^6y=y2+x2. Solve for ∂z/∂x and ∂z/∂y. [b]

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Q: Find the parameters of the linear model using the least squares method, with the independent…

A: Regression Equation: When we want to predict the value of one variable, say Y, from the given value…

Q: Are functions f(x) = x² – 2, g(x) = x² + 2x – 1 and h(x) = 2x² + 6x + 1 linearly dependent? If yes,…

A: Let f(x), g(x) and h(x) are linearly dependent.  So, we can write: Then we compare both sides

Q: Express ax? + bx + c as a linear combination of the functions f(x) = 5, g(x) = 4x, and h(x) = -x²,…

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Q: Find the points of discontinuity for 3(x+2)2 a) h(x) x3 + 4x2 + x- 6 6x- x2 b) f(x) = 9 - x2

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Q: Find the relative maximum or minimum value (if any) of f(x, y) = 2x3 + xy2 + 5x2 + y2

A: The given function is: f(x,y)=2x3+xy2+5x2+y2