12. The function f(x) = ax- x² + bx - 24 has three factors. Two of these factors 2 and x + 4. Determine the values of a and b, and then determine the are x - other factor.

Q: 6. Eliminate the arbitrary constants from the relation y=ax² +bx +c.

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Q: 4. If [æf (x) + 2] dæ = x³ – a² then find the function f (x). 3 A) 2 3 B) 2+ C) 3- 2 E) 2– D) 3+ --…

A: The given equation is x∫x fx+2dx=x3-x2.

Q: 3. Given that f(x) = 3x +3 and g(x) = 2x -6. Determine g[f(x)] %3!

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Q: 12- If f(x)=v3x , g(x)=x/5, and h(x)=6x a. f(h(g(x))) b. f(g(h(x))) c. g(f(h(x))) ·

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Q: Suppose z is implicitly given as a function of x and y, according to The equation: y−zx3=1−yz2 The…

A: Suppose z is implicitly given as a function of x and y, according to The equation: y−zx3=1−yz2 The…

Q: 2 Z= 22,

A: Given  z=2x12+x1x2+4x22+x1x3+x32+2

Q: Is the two functions h(t) and g(t), is h-1g-1 (t) = (hg)-1(t)

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Q: If f(x, y) = 2x+6 (2a-6y) of then is given by:

A: In the above question we will take y as constant since we have to partially differentiate it with…

Q: Solve the equation below giving an explanation. Thanks.

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Q: If f(2) = 15 and f (x) > 2 for 2 s x s 4, how small can f(4) possibly be?

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Q: 9. If f(x) = x2 - 2x + 5, what is f(x+h)? %3D A a2 -2x + h2 - 2h + 10 x2 + 2xh + h2- 2x 2h +5 C a2 +…

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Q: If f(x)= x - 4 and g(x)= Vx-2; which of the following is equal to х — 2 Option 1 – 4(SF 2) X - х — 2…

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Q: 1) If f(x) = - 2x, then f' (8) = A) B) D) 1 E) 3 3x -2 2) If f(x) = , then f'(x) = 2x+1 A) 2 -7 B)…

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Q: 14 7) If f(x) = T4x-5) find f"(x) %3D

A: Given function is- f(x)=14(4x-5)27We need to find f''(x)First we will find f'(x) f'(x)=ddx14(4x-5)27…

Q: 5. Eliminate the arbitrary constants from the relation y = Ae* + Bxe²*.

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Q: Q 4. (a). Show that fog = 4x² - 1, if ƒ(x) = 4x – 5 and g(x) = x² + 1. (b). Show that gof = x + 4\x…

A: Given, f(x)=x+2,g(x)=x2+6 To show: gof=x+4x+10 Solution: f(x)=x+2,g(x)=x2+6 We know,…

Q: If f (x) = x²cos-(x² – 4), what is f'(x)? 2x3 o f'(x) = 2xcos-'(x² – 4) – V 1-(x²-4)² 2x3 o f'(x) =…

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Q: 2 If f(x) = and g(x) then (g of)(x) is equal to x + 3 1 + 3x A x + 3 D 2x x + 3 2х 1 + 3x 2x

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Q: 4) Show that and = are eventually fixed points for the function : 8 0sx< 2– 4x sx< 4х 1 f(x) = 1 4x…

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Q: -x², 5х - 4, 4x* - 3х, 1<x<2 X <0 0 <x<1 If f(x) = then f(x) is discontinuous at x = Зх + 4, x 2 2…

A: f(x) is discontinuous at x if left hand limit not equal to right hand limit

Q: A store is deciding what types of fruit to stock nearest to the registers. They can either stock…

A: Let's find maximum potential revenue fruit.

Q: 14. If Ax) = X+3 and g(x) =x² + 5, what is f(g(4))? 2

A: We know that  (fog)(x) = f(g(x))

Q: (8) If f(x) = x² – 3x, what is f(x +h) - f(x) =? h (x² + 2xh + h²)-3(x+h)-(x²-3x) = 2x – 3 + h (x² +…

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Q: 4. If f(x) = -6x and g(x) = -6x %3D 203 2x+3 and g(x) = 3x 5. If h(x) = %3D

A: The solution are next step

Q: a) Suppose that f(3) = 15, f'(3) – 5 and let H(x) = Vf(x)+ 10. Find H'(3). b) Let f(x) = cx +…

A: (a) Differentiate the function Hx with respect to x to find H'x.

Q: 3. If f(x)=-4x+2 and g(x)=vx 8 find (fog\l12) 4. If f(x)=-3x+4 and g(x)=x find (gof)(-2) 5. If f(x)…

A: 3. Given f(x)=-4x+2 and g(x)=x-8f∘g(12)=fg(12)so now substitute g(12) in given…

Q: Derivatives question: finds f’(x)

A: Given function can be written as

Q: Suppose that a company that makes and sells hand-crafted artwork has a cost function C(x) = 24x +…

A: Use the following formula, to obtain the solution. Profit=Rx-Cx Where x denotes the quantity, Cx and…

Q: Suppose g(x) = x² +2, then g(x+h) will yield to A x+2xh+h2+2 B x²+2xh +h+2 x2 +2xh +h2 +2 x²+2x+h?…

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Q: 2 If f (x) =x² and g(x) =x – 5 then f(g(x))= x² + 25 x² – 25 O x²-5 O x² – 10x + 25

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

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: What are the critical points for the function f(x) = x³ + 9x² + 15x – 8 %3D None x = -1 and x = -5 x…

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Q: How do I find the possible inflection points of f(x)=a/((x^2)+(b^2))? It also states a and b are…

A: To find point of inflection we need to find x from f"(x)=0

Q: if the function f(x)= x^3+ax^2+bx has the local minimum value -2/9 cube root 9 at x= 1/cube root ,…

A: Given fx=x3+ax2+bx has local minimum value -239 at x=13 to find  value of a and b explanation as…

Q: f and g are functions of time, and at time t = 3, f equals 9 and is rising at a rate of 2 units per…

A: It is application of derivative.

Q: Suppose that f(2) = −4, g(2) = 5, f '(2) = −2, and g'(2) = 1. Find h'(2). (a) h(x) = 5f(x) −…

A: Topic - functions and derivative Note - as per bartleby Guidelines,we Are supposed To solve only…

Q: If f(x) = 5x - 2, g (x) = – 2r + 3 and h (x)= x, then (fogoh)(-2)=.... %3D

A: The functions are f(x)=5x-2g(x)=-2x+3h(x)=x3 If f(x) and g(x) are two functions then the composition…

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…

A:

Q: is then the function (2) (x (2x-5) If f(x) = (х-1) and g(x) (x-1) (2x+5) (2x+5) b) () (x) = (2x-5)…

A: The function fg is defined by fg(x)=f(x)g(x)

Q: 2 If f(x) = (x³ +3x)“, what is f'(æ)? O f'(x) = (x³ + 3x) O f (x) = (x³ + 3æ) (3a² + 3) O f'(x) = 2…

A: Follow the steps.

Q: manufacturer finds that the revenue generated by selling x units of a certain commodity is given by…

A: Given query is to maximize the revenue.

Q: 10. The function g(x) = x² − kx³ − 9x² + 7x − 8 has a minimum when x value of k. = 3. Determine the

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Q: f  f(x)=ln(7x^6−3x^2) and g(x)=(π3lne‾‾‾√+13log2(16))5e+x5+6x,  f′(1)=

A: f(X)=ln(7x^6-3x^2)         2nd question is not written proper please write properly and resend

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: 3- For what value of c is the function continuous? Provide a well- communicated solution. F(x) = {…

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Q: 12 Given that f(x) = 5x +4 and g(x) = 7-z, calculate (a) f(g(0))= (b) g(f(0))=

A: Given that, f(x)=5x+4g(x)=7-x2

Q: Suppose that 2 sf (x) < 4 for all values of x. What are the minimum and maximum possible values of…

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Q: If (2)-3.f(2)-1, g(x)=1/x, and htx)-[fx)][g(x)], then what is h'(2)?

A: Given that h(x)=[f(x)][g(x)] So, using the product rule,  h'(x)= [f'(x)][g(x)] + [f(x)][g'(x)] Then…