Suppose that the functionsg and h are defined as follows. g(x) = x+0 h (x) =x² -8 Find the compositions g g and h h. Simplify your answers as much as possible. (Assume that your expressions are defined for all x in the domain of the composition. You de 0 - ()(5 - 6) (h h)() = 0

Q: Consider the following functions. f(x) = 3x + 4, g(x) = 6x - 1 Find (fo g)(x). Find the domain of…

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Q: Consider the function g : R → R given by 3x + 5 if x € (-00, 0) x2 + 6x + 11 g(x) = 5 x + 11 if x €…

A: We will find out the required explicit expression for the function G(X).

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

A: I have provided this answer in step-2.

Q: Calculate the (f(g(x)))' and (g(f(x)))' derivatives if f(x) = x* 1 g(x) = 8x + 1 (Express numbers in…

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Q: Let f(x) = (1/(1+x^2)) a) Find f'(x) using the quotient rule.   b) Notice that f(x) can be…

A: It is required to evaluate the derivative by quotient rule and chain rule for the given functions.

Q: press the given function h as a composition of two functions f and g so that h(x) = (fo g)(x). h(x)=…

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Q: The function h(x) (x + 5)° can be expressed in the form f(g(x)), where f(x) = x°, and g(x) is…

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Q: 7. Let f : (0, 20] → R be given by f(x) = x² – x – 2, and let g : [1, 50] → R be given by 1 g(x) 1…

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Q: Consider the function and its inverse. f(x) = x2 + 4 and f-1(x) = -Vx- 4 When comparing the…

A: f(x)=x2+4f-1(x)=-x-4since f-1(x)=-x-4=x-4≥0x≥4Thus domain of f-1(x) is x≥4and f-1(x)=-x-4range of…

Q: Express h(x) as a composition of two functions: h(x) = 3√(x2 + 1)

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Q: Let g(x)=x^2+3. Find a function f that produces the given composition.  (f o g) (x) = x^2

A: Given information:The given function is

Q: Let g(x) = 7-2x2 be a reference function defined on the interval [-1,3] for a periodic function…

A: Let g(x) = 7-2x2 be a reference function defined on the interval [-1,3] for a periodic function…

Q: Suppose that for all real x S'(x) = -g(x) and g'(x) = f(x). (a) Show that f²(x)+g²(x)= C for some…

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Q: 1) Find the difference quotient of f(x)=x². That is, find f(x+h)-f(x) for h#0. Simplify so h that h…

A: To find the difference quotient of the given function.

Q: If f is a differentiable function and such that and g (x) =x^2 f(x) such that f(3) = -7 f'(3) = 2,…

A: This question can be solved using the concept of product rule of differentiation.

Q: 8.7a | Evaluate a radical function Given the function: f(x) = V3x -4 Find f(0) -2 2 Null set COOO

A: Square root function is defined for x greater than or equal to 0.

Q: if x >0 2. Let f(x) 19(x) if x < 0 (a) Find the formula for g(x) which makes f(x) an even function.…

A: The given function,f(x)=xif x≥0g(x)if x&lt;0

Q: 13. Express H(x): = 14. Express H(x) = 2x-1 as a composition of two functions f and g where H(x) =…

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

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Q: 1 The function h(x) can be expressed in the form f(g(x)), where g(x) = (x + 3), and f(x) is x + 3…

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Q: Given f(x) = - 3x*(x + 2)*(5x + 3) (x – 2)5 List the zeroes (ex. 4, 6, -2): -2,-.2 Degree: 15 End…

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Q: Express the given function h(x) =1/(2x - 3) as a composition of two functions f and g so that h(x) =…

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Q: Let h(x)=f(x)g(x). If f(x)=4x^2−4x+4,g(−1)=2, and g′(−1)=0, what is h′(−1)? Do not include…

A: Given, h(x)=f(x)g(x), f(x)=4x2−4x+4, g(−1)=2  and g′(−1)=0 f(-1) = 4-4+4 = 4 f'(x) = 8x-4 ∴ f'(-1)=…

Q: Find a function f(x) such that f'(x)= −4x^2−8 and f(0)= 4

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Q: 3. Let f : R → R and g : R → R be defined by f(x) = 3x + 5 and g(x) = x² + 7. Find the composition…

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Q: Algebraically show that each of the given combinations are equivalent to the given functions. If…

A: Given query is to find that functions are equivalent or not.

Q: 13. Evaluate the function for the given values of x. (-2181-3 for x -2 f(x)=5x+ 6 for - 2 <x <3 for…

A: Given that the function is

Q: 6. For the given functions f(x) =and g(x) = find the composition and its domain.

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Q: Express the given function h(x) = (x2 + 2x - 1)4 as a composition of two functions f and g so that…

A: To Determine:  Express the given function h(x) = (x2 + 2x - 1)4 as a composition of two functions f…

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: Find the range of f(x)=x-5x+6. O (-00, 1/4] O -1/4, co) O (-00, 00)

A: Range of Quadratic Functions Graphically : The range of a function y = f(x) is the set of values y…

Q: Suppose that the functions h and f are defined as follows. h(x) = x-2 f(x) = = %3D Find the…

A: The given functions are, h(x)=x2-2f(x)=x3

Q: Given the functions fAx) = cos(x) and g(x) = x - 5x- 6, determine the domain of the combined Ax)…

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Q: 1) The function f(x) = x3 - 4x-8.95 has a root in [2,3]. O T F

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Q: Find functions (x) and g(x) So the given function can be expressed as h(x) = f(g(x)). (Use…

A: hx=2x-5x+64 It is the composition of two functions namely, fx=x4  &amp;  gx=2x-5x+6

Q: Please answer a,b,c

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Q: 2 Suppose H (x) = Find two functions f and g such that (f og) (x)=H(x). V 2x+9. Neither function can…

A: Let f(x)=x Let g(x)=2x2+9 Now f○g(x)=f(g(x)) therefore, f○g(x)=f(2x2+9)=2x2+9 which is same as H(x)…

Q: Suppose that the functions g and h are defined as follows. g (x) = 5x 4 , x* 0 %3D h (x) = 7x-3 Find…

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Q: For the given functions f and g , find the indicated composition. g(x) = 2x - 5 f(x) = 4x + 2x + 8,…

A: Given that,

Q: If f(x) = x³ + 1.5x290x+16, find analytically all values of a for which f'(x) = 0. (Enter your…

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Q: Consider the function h(x) = x² In(x³) with h'(x) = 2x In(x³) + 3x and h" (x) = 2 ln(x³) + 9. 4.1…

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Q: 1. Given f(x) S(x) = x² + 4x - 2 and g (x) = 3x – 4 , find the composition of functions for the…

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Q: Suppose H (x) = 2 x +7. Find two functions f and g such that (f g)(x)=H (x). Neither function can be…

A: We have given Hx=2x13+7We have to find two function f and g such that f∘gx=Hx

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: Suppose the function f(x) has a domain of all real numbers and its derivative is shown below. f'(x)…

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Q: 6. Given the functions f(x)=√x+5 and g(x)=√x²-4, a) Determine (fg)(x). b) Determine the exact value…

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Q: Let h(x) = f(x)g(x). If f(x) = –3x² + 2x – 3 and g(x) = –3x² + 4x + 3, what is h' (1)? Do not…

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Q: Let h(x)=f(x)g(x). If f(x)=−3x 2−4x+2 and g(x)=−x2 +3x+2, what is h′(−1)? Do not include "h′(−1)="…

A: Consider the function