The composition of the function f with the function g is written as fog and is defined by fo g(x) = f(x) g(x)" f(g(x)). f(x) + g(x). f(x) – g(x). g(f(x)). f(x) • g(x).

Q: 7. For the function f (x)=(x-2)° +1, a. Sketch the graph of over the interval [0,3].

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Q: The critical points of the function f(æ) = 9x2 – 2x4 occur at x = 0, x = +1.20 0, a = +1.50 %3D %3D…

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Q: The function h(x)% = can be expressed in the form f(g(x)), where g(x) = (x + 3), and x + 3 f(x) is…

A: Given query is to find the function f(x).

Q: Consider the function f(x)=2x3+9x2−108x+5,  −6≤x≤4f(x)=2x3+9x2-108x+5,  -6≤x≤4. Use the derivatives…

A: Given, f(x)= 2x³+9x²-108x+5 -6<=x<=4

Q: Given the functions fAx) = x - x and g(x) = x- 1, determine an equation for the combined Ax) y =…

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Q: Let h(x)=f(x)g(x). If f(x)=3cos(x) and g(x)=3x3 +2x2 −x+4, what is h′(x)?

A: f(x)=3 cos (x) g(x)=3x3+2x2-x+4 h(x)=f(x) g(x) We need to find h'(x)

Q: Find the maximum and minimum values of the function f (x) -3x on the interval 1+x2 0<x<6.

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Q: Express the given function h as a composition of two functions f and g so that h(x)= (f o g)(x),…

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Q: 17. Find the composition of two functions f(x) with g(x) a) f (x) = x³ - 9 and g(x) = V(x – 3)² b)…

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Q: 1. Consider the function f(x) = -x² + 6x and the point P(2,8) on the graph of f.

A: Given data: The expression for the given function is f(x)= -x2+6x. The given point is A(2,8). (a)…

Q: Let h(x)=f(x)g(x) where f(x)=−4x^2−5x+1, g(1)=−5, and g′(1)=−4 what is h′(1)?

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Q: you agree with the contention that the functions f(x)= x +2 and g(x)= x2 -4/x-2  are the same in…

A: Yes i agree with the contention that the functions f(x)= x +2 and g(x)= x2 -4/x-2  are the same in…

Q: The function h(x)= 1 over x-8, can be expressed in the form f(g(x)), where g(x)= (x-8) , and f(x))…

A: use composition of function to find the function f(x).

Q: Discuss the continuity of the function on the closed interval.

A: Given: f(x)=x2-1x+1 The function is continuous at a point if the function returns a unique value…

Q: What is the change of y with respect to x of the function s(x) = (3x¹ + 9x³)(x² - 6x +9) ? -9x²…

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Q: 1. a) If f(x) = x-2x + 1 and g(x) =1, find f( g(-2) %3D

A: givenfx=x3-2x+1  and gx=1x2

Q: Find the absolute maximum and minimum of the function f (x) = x³ - x+2 on the interval [0, 3] %D

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Q: f(x, y) = /4 – x² – y² + V1 – x? -

A: To find the domain of the function, f(x,y)=4-x2-y2+1-x2

Q: 1. For the function f(x) = 3x² - 5x +7 find: a. f(-2) %3D b. f(-a)

A: Please see the below picture for detailed solution.

Q: 1. Use f(x) = 5-x and g(x): to find the following and identify its domain: %3D x-2 a) (f g)(x) b)…

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Q: If f(x) is a differentiable function such that f'(-2)=-1 and g(x)=f(3x+1), then what is g'(-1)?

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Q: 2 For the function f(x) = -x', find f'"(x), f'"(0), f'"(1), and f"(- 1).

A: To find the double derivative for the given function.

Q: Over the interval (0,2), the function f(x) = (-x²) e*

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Q: Determine whether the function of f(x) is continuous at x = -1 x2 -1 f(x) ={ x +1 X + -1 -2 X = -1

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Q: Assuming f of g = 1/x + 1 and if g(x) is x +1. Find f(x)

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Q: The function h(x) ==x-1 represents the composite h(x) = f(g(x)). If f(x) = 2x – 1, what is g(x)?

A: Please refer the attached image for complete solution. Given : hx=43x-1, hx=fgxfx=2x-1To calculate :…

Q: Let f(x) be a polynomial and g(x) = f '(x) be its derivative. If the degree of (f(x) + f(-x)) is 10,…

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Q: 4. Find the functions f(x), g(x),h(x) that satisfy: f(g(h(x))) = 2.

A: A composite function is created when one function is substituted into another function .

Q: Find two functions f(x) and g(x) such that f(g(x))=x but g(f(x)) does not equal x

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Q: Use Intermediate Vaule Tun to show that the functions f(x) = x^3 and g(x) = 2x + 3 intersect at at…

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Q: Make the composition (f o g) (x) with the function f (x) = x ^ 2 + 2 -2 and g (x) = √x

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Q: Consider the compound function:             (x - 2)3 for x less than or equal to 2 h(x) =  |x| for…

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Q: Please show step-by-step solution

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Q: For the real-valued functions f (x)3D2x-1 and g (x) =Vx-4, find the composition f og and s

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Q: Show that the function g(x) =x |x | has an inflection point at (0,0) but  g " (0)  does not exist.

A: Given function:                                 g(x)=x|x|   To find out the Inflection point=?…

Q: f(c) {}} [=+3 = < (3x + 1

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Q: The function h is defined by h(x) = x^2 +2. find h(5z)

A: Given h(x)=x2+2

Q: Let h(x) = f(x)g(x). If f (x) = 3x² – x – 4 and g(x) = -x² + 2, what is h' (-1)?

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Q: The function h(x)=1x+7h(x)=1x+7 can be expressed in the form f(g(x))f(g(x)) where…

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Q: Sketch the graphs of the function f(x) = cos x. y y 2 2 f X 3X -27 2 -2- -2- y y 2- f X -27 - 2 2 -1…

A: We know, cosx = 0, if x =(2n+1)π2; n∈ℤcosx = (-1)n, if x =nπ;  n∈ℤ

Q: 8. For the function f(x)=3x+5-11, find the values of x such that f(x)=0.

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Q: Let h(x)=f(x)g(x). If f(x)=2x2+1,g(1)=0, and g′(1)=−1, what is h′(1)?

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Q: Find the X-coordinate of the points of intersection of the graphs of two functions. f (x) = x² – 11x…

A: Find the x-coordinate of the points of intersection of the graphs of two functions.…

Q: Express the given function h(x) = 3√(x2 - 9) as a composition of two functions f and g so that h(x)…

A: Given function is  h(x)= x2-93.

Q: 6) Find the value of c such that {0, c} is 2-cycle such that c be a constant and let the function be…

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Q: Evaluate f''(c) at the point. f(x) = (x2 - 5)(x3- 5), c = 1

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Q: Do you agree with the contention that the functions f(x) = x + 2 and g(x) = x − 4/x − 2 are the same…

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Q: 3. Find the value of the constant k that makes the function continuous f(x) = {x² – 6, x + 4k, x 6

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Q: The function h(x)=1 (fraction) x+9 can be expressed in the form f(g(x)), where g(x)=(x+9), and f(x)…

A: ANSWER : f(x) = 1/x   EXPLANATION :

Q: Find extreme values of the function over its natural domain. (a) f(x) = x³ + x² – 8x + 5 (b) f(x) =x…

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