The functions f, g, and h are defined as follows. f(x) = |-13+4x| g(x)= x +3 8 (6) h (x)=/1+7x %3D Find f 3 g(3), and h (2).

Q: The critical points of the function f(x) = a2– 14x + 12 are

A: Given function is f(x) = x2 - 14x + 12 Critical point of the function is the point in the domain…

Q: The function f(x) = = a) 0 b) 1 Oc) 2 d) 3 (x² + 1) (x² + 2) has how many x-intercepts?

A: Given function:- fx=x2+1x2+2

Q: F(x)=3x^2+2x-7 , G(x)=4x-5x^2+3x: Find G(x)-F(x)

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Q: 3. Find f'(x) for f(x) = v5 + e2x xe2x-1 А. V5+e2x 1 2v2e2x С. 5+ e2x e2x D. V5+e2x V5+e2x B.

A: In this question, concept of chain differentiation is used in this question.

Q: Given the function g(x) = (x – 1)(z + 2)(z - 3) its g-intercept is its -intercepts are

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Q: If c is a non zero constant then the function is always differentiable x2 + c2

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Q: 1. If f(x) = x-1 and g(x) = 2x, what is g(f(x))? c. 2x -1 %3D а. х-2 b. 2х-1 d. 2x-2

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Q: f (x + h) – f(x) - With f(x) = 5x² – 3x + 2, find h

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Q: G' (x) = 2xex + x 2ex, and this is not equal to f (x). However, H'(x) = 2ex + 2xex - 2ex = 2xex = f…

A: Given Data The derivative function is G’(x)=2xeˣ+x2eˣ. The another derivative function is H’(x)=…

Q: f(x) = 3x + 5 g(x) = 4x² – 2 %3D h(x) = x² – 3x + 1 Find f(x) - g(x) – h(x). O - 5x + 6x + 6 O -5x +…

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Q: Find f′(x) and f′(c). Function f(x) = (2x2 − 3x)(9x + 4) Value of c = −1

A: f(x) = (2x2 − 3x)(9x + 4) c = −1   f'(x) = (2x2 − 3x).(9x + 4)' +  (2x2 − 3x)'. (9x + 4)        =…

Q: The function f(x) = 2x³ – 36x² + 192x - 3 has two critical numbers. The smaller one is x = and the…

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Q: Find the value(s) of x for which f(x) = g(x). f(x) = x4 − 2x2, g(x) = 2x2

A: To find the value(s) of x for which f(x)=g(x). f(x)=x4-2x2,g(x)=2x2 Solution:…

Q: f(x) = √√√5x - 2, g(x) = x² - 25, and h(x) (fh)(x) = 1 x - 3

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Q: (c) f(x) = x4 - 1 and g(x) = x4 – x³ – 3x² + 5x – 2 in F(R) -

A: HEre we have to find the GCD of the given polynomIal.

Q: The cost and revenue functions for a certain firm are given by C(x) = 14x + 20,000 and R(x) = 22x,…

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Q: 3 na of the function f(x) =x3 -x2 - 6x + 12, -3 < x< 3. 2

A: Solution of the problem as follows

Q: Can you check it please?

A: To verify thesteps in the  simplification

Q: Given that f(x) = 3x – 1, g(x) = 2x and h(x) = x + 1, determine: a. hgf(x)  b. hgf(-2

A: Given : f(x) = 3x-1             g(x) = 2x             h(x) = x+1  To Find : hgf(x)…

Q: If f(x) =−3x + 2 and g(x) = x² − 3x + 5, find: a) fog(x) b)go f(x)

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Q: The function f(x) =x³ – 3x2 + 3x -1, x e R has a point of inflection | at A) x = 1 B) x =-1 C) x = 3…

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Q: 2. 1. f (x) = x° – 4x – 5 g(x)3Dx5 a) Find(-)æ x + 5

A: Consider the functions

Q: If f=x-2x-3 &g(X)= 1| then find a) (fog)(x) b) (gof) & (x)

A: To find (fog(x) and (gof)(x), we use the definition of composition of two functions.

Q: Given f(x)=x– 2x-8, g(x)=5x -1 and h(x): %3D

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Q: If f(x) = x³ – 2.x² +3 , the only point where f could change the concavity is 2 b) x =- 3 a) x =- c)…

A: Finding the inflection points

Q: If f(x) = 3x-1 +4 and g(x) = 4x-7, what is (f- g)(x)? %3D O A. (f-g)(x) = 3x-1 - 4x- 3 %D B.…

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Q: 1. Given f(x) = -2x and g(x) = x - 7, find g(f(2)). *

A: f(x)=-2x g(x)=x-7

Q: 7. Given the function 8(x)%3D4X' - 3x² +x-1, find g(0), g(-1), and g(x-x) |

A: Some important formulas (a - b)3 = a3 - 3a2b + 3ab2 - b3 (a - b)2 = a2 - 2ab + b2

Q: The critical points of the function f(x) = 4x³ – 48x +1 are a. 2,– 2} b. d.

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Q: f(x) = g(x) + h(x), where g(x) = 2x 4 + 12x2 + 4 and h(x) = -5x 3 - 3x

A: Given gx=2x4+12x2+4hx=-5x3-3x fx=gx+hx

Q: The Cost function C(x) and the Revenue function R(x) of a firm are given by C(x) = 4x +1200 and R(x)…

A: Given that the cost function Cx=4x+1200 and the revenue function is Rx=10x. We have to find the…

Q: f(x)=x2-2x+4     g(x)=x2+2x-4 (f o g)(4)

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Q: Find the range of f(x)=x-5x+6. O [-1/4, 0)

A: The given function is:fx=x2-5x+6To find the range

Q: 2. GIVEN g(x) = / x³-3x² + 3x-1/. FIND g (-4)

A: Formula: (a-b)3=a3+3a2(-b)+3a(-b)2+(-b)3 (a-b)3=a3-3a2b+3ab2-b3.

Q: If f(x)=5x-1, g(0)=2, g'(0)=4, and h(x)=f(g(x)), then what is h'(0)?

A: Given that h(x)=f(g(x)) Using chain rule we get: h'(x)= f'(g(x))g'(x) We plug x=0 So, h'(0)=…

Q: Find Critical numbers of the given function: x² +5 f(x) = %3D x - 2

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Q: Given f(x) 3D4X-6 and g(x) = 2x 3x SPO find (f-g)), +g), (S.g))

A: Given that, fx=4x-6 ; gx=2x2-3x We have to find, f-gx ; f+gx ; f·gx ; fgx

Q: Find h'(-3) if h(x)=4g(x)-5f(x), f(-3)-7,and g'(-3)=-2. Oh'(-3)-0

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Q: f (x) = 2x² + 3x – 4, g(x) = 2x – 1. Find (g •f)(x) -

A: Given,          fx=2x2+3x-4          gx=2x-1

Q: b. Given f(x) = 3x + 2, g(x) = 2x² – 4x and h(x) = x-x+ 7, find (g + h) (-1/2). %3! %3D

A: Given: f(x)=3x-2, g(x) = 2x2 -4x and h(x) = x2 -x+7 To find: g+hf-12 This can be defined as follows:

Q: The domain of the function f(x) Зх-12 is V2x-4 %3D a) {x/x > 4 and x + 2} b) {x/x > 2 and x # 4} c)…

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Q: Given f (x)= 2x +1 and g (s3)=x*+2x-1, find (I+g) (3).

A: (f+g)(x) = x2+4xexplanation is given below

Q: find g'(3) given that f(3) = -2, f'(3) =4, and g(x) =2x+1/f(x)

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Q: Find f′(x) and f′(c). Function f(x) = (x3 + 4x)(3x2 + 2x − 5) Value of c = 0

A: Given:fx=x3+4x 3x2+2x-5  To Find: f' (x) and f' (c)

Q: 2 Given f(x) = x“ - 2 and g(x) 4x + 1, find a. f g b. g(f(x))

A: We will find f .g and g(f(x)) in the following step.

Q: g(x)=3x-4g(x)=3x−4, find g(1)g(1).

A: we will do simple calculation

Q: Given f(x) = 3x- 5x+4, g(x) =- 3.x and h(x) = V2-x , find x-2 a) f(3), f(-3), g(2), g(-2), h(1),…

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Q: 1. If f(x) = 3x + 9 and g(x)=x²-4, find: a) (fog)(x) c) (gof)(x)

A: A detailed solution is given below

Q: For what value of x does the function f(x) = x³ – 2x² + x -11 have a relative maximum? -1/3 1/3 -1

A: Using application of derivatives.

Q: For what value of x does the function f(x) = x³ - 2x2 + x – 11 have a relative maximum? A 1/3 B 1 ©…

A: