Refer to the following functions g and h. g(n) = n² +n h(n) = n² –n Evaluate each function below: a) (h + g)(n) b) (h – g)(n) c) (h g)(n)

Q: 2. Use the table to write a function rule for h(x). -3 -2 -1 1 -3 - ( f(x)=2x+1 g(x)=5x – 6 -21 -16…

A: Introduction:- A function is an expression, rule, or law in mathematics that defines a relationship…

Q: compute f(x)-f(a)/x-a for the following function f(x)=x^2-3x+1

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Q: ALL of the following are not types of functions except. а. one - to - many b. many - to - one c.…

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Q: Use the following graph of f(x) to describe the behavior of f '(x). State where f '(x) is positive,…

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Q: Which of the following constitute the values of domain of f(x)=

A: domain is the value of x for which function is defined.for exa if function value is f(x)=√x-2 so…

Q: Let k(x)=f(x)g(x)h(x). If f(−2)=−5,f′(−2)=9,g(−2)=−7,g′(−2)=8,h(−2)=3, and h′(−2)=−10 what is…

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Q: Consider the following. f(x) = 2x/ 16 – x², [-4, 4] (a) Use a computer algebra system to…

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Q: 3. Consider f(x) = Vx and g(x) = x3 + 2, construct the following function. g(f(x)) f(x) g-'(x)

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Q: 4. Select all the true statements about the end behavior of the function f(x) = -x*-5x .4 + 5x +3.…

A: Given :

Q: 5. Check the following boxes to indicate if each of the following is true or false. Function T F…

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Q: The function h is defined by the following rule. h (x) = 9. Find h (x) for each x-value in the…

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Q: ALL of the following are not types of functions except. O a. one - to - many O b. many - to - many O…

A: We have to find which is not a type of function.

Q: The functiong is defined by the following rule. 19 = (x) 8 Find g (x) for each x-value in the table.…

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Q: Below is the function f(x). 5 4- 46 -5 -4 -3 -1 -1 2 3 4 5 -2 -3 -4 -6 -7+ Over which interval of x…

A: The graph of the function is given by

Q: Consider the following. f(x) = 2x/4 – x², [-2, 2] (a) Use a computer algebra system to differentiate…

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Q: 2. Define the following functions: f(x) = x - 5x + 25 a.

A: From the question, it is clear that the function can take input as any real number, Therefore…

Q: Define H(x) as a piecewise defined function and evaluate H(1), H(2), H(3), H(0) and H(-2) given by,…

A: We have to solve the problem by just putting the value in the piecewise function.

Q: 10) Suppose that the functions f and g are defined as follows. fx) = -5x² + 2x g(x) = 3x – 2 Find()…

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

Q: Which of the following statements is true about the function f(x) = 6x2- x? O a. The graph of f is…

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Q: Which of the following is TRUE for the function g(x) = x^2-2x? O g(x) is increasing on (-infinity,…

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Q: Determine the formula for the the function f below. p(x) 1 1 - 1 12 1 3 72 1 4 432 2.

A: when x=1 p(x)=12=3·16 when x=2 p(x)=112=3136=3162 when x=3 p(x)=172=31216=3163 when x=4…

Q: Suppose that f (x), g(x), and h(x) are functions such that f (x) is Θ(g(x)) and g(x) is Θ(h(x)).…

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Q: 3. Let f : A → B. Then 1gf = f and f14 = f. Hint. You may use the fact that fg, for functions f, g,…

A: Let               f1 : X→Y , f2 : X→Y be two functions, then we say that the functions f1 and f2 are…

Q: Let f(x)= -x - 1, h(x)= -x+2 Find ​(h◦​f)(3​)=

A: (h◦​f)(x​) = h[f(x)]

Q: What is the end behavior of the given function? f(æ) = –12Va As x → 0, f(x) → -o. As x → -0, f(x) →…

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Q: 11. What property must f(x) have in order for f'(x) to exist?

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Q: Consider the following functions. f(x) = √√√√64 - x², g(x): = √x + 2

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Q: 3. Write the function F (x) = x3+6 as a composition of three or more non- x3 identity functions.

A: The given function is, Fx=x3+6x3-9

Q: Consider the following functions f (x)=x²-1 and g(x) = 2 - x Evaluate fog (-7)

A: NOTE: Refresh your page if you can't see any equations. . given functions are

Q: Consider the functions: f (x) = 3x – 1; g(x) = 1– 2x Compute fo g(-26) exactly

A: The given function is  f(x) = 3x-1  g(x) =1-2x  We have to calculate f(g(-26)).

Q: For  f={(2,4),(3,−2),(−5,−5)}f={(2,4),(3,−2),(−5,−5)} and g={(−3,1),(−2,5),(3,−2) ou were asked…

A: For two functions f and g, (f+g)(x)=f(x)+g(x)

Q: Consider the following function: f(x)=x^3+2x^2-8x-3 b. Find the extreme values ​​of f.

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Q: Consider the following piecewise function. x<2 f(x) =- 4*-3, 25x<7 x27 1, (-2x +7, Part A: Evaluate…

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Q: 7. Give an example of two functions h(x) and g(x), such that (h o g) (x) does not exist.

A: we need to find two functions h(x) and g(x), such that (hog)(x) does not exist. Let us take two…

Q: Let the function fx=eax Where a= (last three digits in the form 1.23) X 1 3 4 f(x) . Complete the…

A: Given function f(x)=eax where a=1.23 So f(x)=e1.23x. The objective is to complete the table and…

Q: How many one-to-one functions f: [4] to [6] have 5 not in the range of f?

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Q: Consider the following function: f(x) = 2 8 - 9 - Step 1 of 4: Determine f'(x) and f "(x).

A: on differentiation we get

Q: Characterize the following function in terms of notation. (a) f(n) = (n² + 2)(10n³ +5n-6)n¹, n ≥ 0.…

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Q: Let f(x) be the function x + 5 for x 2.

A: Let f(x)=x+5 for x&lt;-1               =cx for -1≤x≤2                =x+6 for x&gt;2 To find the…

Q: (b) Let the function h : Z12 → Z12 be given by the rule h([x]) = [3] © [x]. (i) Compute h([5]). (ii)…

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Q: b. Suppose the function h is defined as h(x) = 3f(x). Determine the domain and range of h.

A: b. Given that  h(x)=3f(x) Domain of f is [0,4] and range [0,2]

Q: 39. Let f(x) = 2x3 - 4. Find a function y = g(x) so that (f o g)(x) =x+2.

A: We use the definition of composition of functions to find y= g(x).

Q: Determine the end behavior of the following monomial functions. (That is, does the function output…

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Q: Find the domain of the below function: g(x)=In(x-x²)

A: For a function, y=f(x), the set of real values of x for which f(x) is defined is called the domain…

Q: Consider the following function: 4х 7x -20 1 -1 f(x) = 3 -7x 20 7 2 -X 11 0 0 1 a) What is the…

A: Calculate the value of determinant to find f(x) in simple form.

Q: Consider the following function: За 10x -17 1 -1 -10x 17 10 f(æ) = 3 2 -x 13 1 a) What is the…

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Q: Let h(x)=f(x)/g(x), where f(−3)=7,f′(−3)=−9,g(−3)=−2, and g′(−3)=1. What is h′(−3)?

A: Given query is to find indicated derivative.

Q: 4. Evaluate the difference quotient, (f(x + h) − f(x))/h for the following function: f(x) = 4/(x-2)

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Q: Let h(x)=f(x)g(x). If f(x)=x^2+4x−1,g(−2)=3, and g′(−2)=−5, what is h′(−2)?

A: We have to find function

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: