Let f(x) = |x + 1| +1 and g(x) = væ + 2 + 1. Let h be a function with the following properties: the domain of h is [ – 4, 8), the only solutions to the equation h(x) = 0 are æ = 5 and h(2) = 3. Part A. Explain and demonstrate how to find the domain of (f + h). Part B. What is the domain of (f + h)? Write the answer in interval notation. Part C. Explain and demonstrate how to find the domain of (유) )? Write the answer in interval notation. h Part D. What is the domain of Part E. Compute () (2)

Q: Let h(x)=f(x)−g(x). If f′(−2)=−8 and g′(−2)=1, what is h′(−2)?

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Q: Let h(x) = f(x) – g(x). If f(x) = 5x² and g(x) = 2x³, what is h' (1)?

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Q: . The graph of the function f(x) = ax2 + bx + c has vertexat 10, 22 and passes through the point 11,…

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Q: 1. What is the domain of the function f(x) = V 36 – x' ?

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Q: Find the absolute extreme values of the function on the interval. F(x) = Vx, -27sxs8

A: We will first differentiate the function to find the critical points.

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

Q: Let h(x)=f(x)−g(x). If f(x)=9x^2 and g(x)=8x, what is h′(−5)?

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Q: f(x)%3DX²-2x+5

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Q: Find the range and domain of the function, f(x,y) = sqaure root of (36-x2-y2)

A: Given function is f(x,y)=36-x2-y2We have to find the domain and range of…

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Q: 22 Which value of x is NOT in the domain of the function f(x) %3D 11x 33 -

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A: Domain is the set of all values that can be taken by x so that the equation is defined.

Q: 2 2 V1-x 1-х

A: ∫un du = un+1n+1+C ∫cos(au) du =1asin(au)+C

Q: Q2// Sketch the graph of the function defined by the formula 0, x<-1 f(x) = {V1- x2 ,-1<x<1 x 2 1 X…

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Q: The fixed-points of f(x) = (x² + 2) are_ and

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Q: For what value of x does the function f(x) = x³ – 3x? attain the absolute maximum in the interval…

A: We have to find Absolute Maximum in the interval [-1,4] by Second Derivative Test.

Q: 7. Find the natural domain of the function f(x) = V4– 3x .

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Q: Consider the function 3 2 f(x) = 2x + 18x – 162x + 3, - 9 < x < 4. This function has an absolute…

A: Given, f(x)= 2x³+18x²-162x+3 -9=&lt;x=&lt;4

Q: Let k(x)=f(x)g(x)h(x). If f(x)=−2x−3,g(x)=−3x+3, and h(x)=−3x2+x+1, what is k′(1)?

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Q: Let h(x)=f(x)+g(x). If f(x)=x4 and g(x)=6x3, what is h′(−3)?

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Q: Rewrite h(x)=- Vx+3 in terms of f and g. 3.

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Q: The fixed-points of f(x) = (x² + 2); are and

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A: Given function is f(x)=sech-121-xk Since sech-1x=ln1+1-x2x here, 1+1-x2x≥1 ⇒ either x≥0or x≤1

Q: The fixed-points of f(x) = (x² + 2) are and

A: Solution :  The fixed point of the function f(x) is  f(x) = x  Since, given function is  f(x) = 1/3…

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: Let h(x)=f(x)+g(x). If f(x)=6x and g(x)=3x2, what is h′(−1)?

A: Add the given two functions and differentiate with respect to x

Q: (a) By sketching the graph of the function f(x) = x³ + x² – 1, show that the equation f (x) = 0 has…

A: The root of the equation is 0.755 Also it is evident that it is lying between 0 and 1

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A: B belongs to [2,3]

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Q: Consider the function f(x)=2x^3+27x^2-60x+1, -10≤x≤2. Find the absolute minimum and maximum value…

A: Answer and explanation is given below..

Q: Consider the function f(x) = 2x + 21x- 108x + 4, - 9 < x < 3. This function has an absolute minimum…

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Q: Let h(x)=f(x)−g(x). If f(x)=5x2 and g(x)=2x3, what is h′(1)?

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Q: A- Find the averag value of the function f(x)=x+ B- Find the aree √x²+2x on(2,4).

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Q: Given that 2x ax + 4 C then find the solution x and enter your answer as a function of a, b, c in…

A: Using cross multiplication.

Q: The domain of the function f(x, y) = In(-x² -+1) is: 4 x² + 4 x² + y? > 4 1 x² + y2 <4

A: See the attachment

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Q: By expressing the function f(x) = 3x2 - 6x + 5 in the form of f(x) = a(x - p)2 + q, find the…

A: For the detailed solution of the problem follow the next step.

Q: Find the range of f{x}=x² +5x+6. O (00, 0) O (o, -1/4] O -1/4, )

A: Topic = Functions

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A: (c) In this question, we have to use the property of the Heaviside unit step function about t=5.…