Let 15 ƒ(x) = (2x² + 3)¹ (2x² + 7) ¹5 Find the derivative and write the answer in factored form. ƒ'(x) =

Q: 1. Let f(x) = 2x² + 1 and g(x) = [x]. Find the following. (a). What is (f ○ g)(x) = f(g(x)) = = (b).…

A: We Know that,  Greatest Integer Function is a function that gives the greatest integer less than or…

Q: 5. Let f(x) = x² + 3x and g(x) = 2-x. (a) Find (f - g)(x) (b) Find (fg)(2) (c) Find (4) (x) and its…

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Q: Let f(x) = (x-9)7 – 8, determine f¯¹(x). - ƒ¯¹(x) =

A: To find the inverse of the function f(x) = (x - 9)7 - 8, we need to express x in terms of y, where y…

Q: 25. For the function f(x) = 45x3 - 3x5, determine the interval(s) for which f(x) decreases. O (3, 3)…

A: We will solve this question by  differentiating f(x) and then finding the intervals for which the…

Q: 4. Let f(x)=1+x³-x. Find an x-value that makes f(x) 0.

A:

Q: Suppose f is differentiable on the set of real numbers R and a E R. Let F(x)= f(xª) and G(x) =…

A: F(x)=f(xα)F'(x)=f'(xα)ddx(xα) , [chain…

Q: Show that f[x0, x1, x2] = f[x2, x1, xo].

A:

Q: f(x) = 8+x 8 - x on [4, 6].

A:

Q: 5. Which of the has a domain of (-o, +c0)? a. f(x) = x b. f(x) = x2 c. f(x) = x d. f(x) = x*

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Q: Using a table, Find f [1.3, 2.4, 3.6] where f (x) = x²

A: For a function, , x is the independent variable and y is the dependent variable.

Q: Given the function fA(x) = x², g(x) = 3x – 4, find the composite function gof (where gof'means…

A: I have find inverse of f the composition

Q: IfY C X, show that inf (X) < inf (Y)

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Q: 11) For the function f(x)x+3 a) Find f(1) and f(m +6) b) Find the domain

A: We have been given a function and we are supposed evaluate its value for the given value/expression…

Q: (-x if x < -2 4. Let f(x)=x² if-2<x<2 Compute the following function values: (0 if x ≥ 2 a) f(-3) b)…

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Q: f (x) = -x² + 5æ, [0, 5]

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Q: 11. State the inflection point of f(x) = Vc-7+8. O A. (8, 7) B. (-7, -8) O C. (7, 8) O D. (-7, 8)

A: Point of inflection

Q: Consider these functions. 1) Evaluate (f + g)(2). f(x) = 3x² – 5 g(x) = Vx - 2 A) -1 B) 0 C) 3 D) 7…

A: we have the given functions  f(x)=3x2-5 g(x)=x-2 1) (f+g)(2)=f(2)+g(2)…

Q: What are the valuesbof x where tge functions f(x) = (3x+2)(x+1)\x+3 is undefined?

A: Consider the function f(x)=(3x+2)(x+1)x+3

Q: What is the domain of the function f (x) : (-1,0) U [1, 00) b. (-1,0] U (1, ∞) c. (-00, –1) U [0,1)…

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Q: 5. Let f(x) = 2x³-x² +7, find: a) ƒ(2) b) f(-5) c) f(a)

A: “Since you have posted multiple questions with multiple sub parts,we will provide the solution only…

Q: Determine F(x) if, for all real x and y, F(x)F(y) – F(xy) = x + y.   Hint:  What could F(1) be?

A: Consider the provided question, We have to find F(x).

Q: 7. Consider function below. What is the value of fl-5); f(0); 3) respectively? (4x+11, -10 Sx<-2 fx)…

A:

Q: 4. For the functions f(x) = Vx -3 and g(x) = Vx+2, find and detemine the domain in ease case. a. gf…

A:

Q: 4. For f(x) = x² – 3x, evaluate a) f(2) [2,3,3] c) the value of x when f(x) = 4 b) f(m + 1)

A: Given,              f(x)=x2-3x

Q: Find the range of the function f(x) = x2-1 O [-2,21 R\[-1] R\{0}

A: Range of function

Q: 21. What is the domain and range of f(x) = V– In x ?

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: 4. Let f(x) = g(x) = x -5, k-(10) +7 = 10 and h (x) = find: ther b. Domain of h(x). c. (hof)(2). (Z…

A: (NOTE:   As nothing is mentioned, so all functions are taken as real valued functions.)

Q: 2. Let f: RR by f(x) = -2x + 1. Let A = [2,5] B = [-1,3] C = [−2,3] D = [1, 4]. Find each of the…

A: Here are the solutions:  Note:We have provided the best possible solution for you. Kindly, verify…

Q: Two functions f, g are defined as follows: Find a) ƒ-¹(2) b) (gof)(-4) f(x) = 3x + 5 g(x) = 2(1-x)

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Q: (x+1)(x-2)². On what interval (2) (x - 5) let g"(x) = is g Concave up? (Note: you are given g" but…

A: g''x=x+1x-22x-5

Q: Let f(x, y) = Evaluate f(5,5) 175 - 3x² - 4y2

A: