Suppose f, g, h, and j are functions such that: f(r) represents the circumference (in cm) of a circle whose radius is r cm. • g(C) represents the radius (in cm) of a circle whose circumference is C cm. h(r) represents the area (in cm²) of a circle whose radius is r cm. j(A) represents the radius (in cm) of a circle whose area is A cm?. a. Use function notation to represent the area of a circle whose circumference is 130 cm. h(g(130))=1345.54 Preview b. Use function notation to represent the circumference of a circle whose area is 5.17 cm?. 8.05 Preview

Q: A hemispherical bowl of radius 9 inches is filled to a depth of h​ inches, where 0≤h≤9. Find the…

A: Explanation and solution is given below....

Q: Consider the functions f(x) and g(x), for which f(0) = 2, g(0) = 5, f'(0) = 10, and g'(0) = 5. Find…

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Q: If f:X → Y and g:Y → Z are one-to-one functions, then the composition f •g is one-to-one function.

A: f:X→Y and g:Y→Z are one-to-one function

Q: Given f (x) =x-4 and g (x)=|x+2|, what is the domain of the quotient function f/g?

A: Domain will be  Whole real numbers except 2 Explanation is given below......

Q: The monthly sales for January for a whole foods market was $60,000 and has increased linearly by…

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Q: For the function defined as follows, find (a) f(x+h)-f(x), and (c) f(x+h)-f(x)/h f(x)= 10/x   (a)…

A: We have given the function;

Q: For the function defined as follows, find (a) f(x+h)-f(x), and (c) f(x+h)-f(x)/h   f(x)= 3/x (a)…

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Q: Draw the graph of the function f :R → R defined by f (x) = x3, x∈R.

A: We will make a table for f(x)=x3 x -1 0 1 y -1 0 1

Q: Suppose H (x) = (2-2x)*. Find two functions f and g such that (f og) (x)=H(x).

A: H(x)=(fog)(x)=f(g(x))

Q: If f(x) and g(x) are two functions defined by f(x) = √(x + 1) g(x) = | x - 1 |, then what is the…

A: To find f(g(9))

Q: Express h(x) = (x2 - 3x + 7)9 as a composition of two functions f and g such that h(x) = ( f ∘…

A: To Determine:  Express h(x)  as a composition of two functions f and g such that h(x) = ( f ∘ g)(x).…

Q: Find a simplified form of the difference quotient for the function. f(x) = (x- 8)(x+h-S) (x -…

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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: Find (fog)(x) and (gof)(x) from the following functions:  • f(x) = 4x + 3 and g(x) = x - 1  • f(x) =…

A: Given:-  • f(x) = 4x + 3 and g(x) = x - 1  • f(x) = 2 - x and g(x) = 3x + 4  • f(x) = 3x + 1 and…

Q: 1. If f(x) = x + 5 and g(x) = x – 5, (a) f(g(x)) = (b) g(f(x)) (c) Thus g(x) is called an function…

A: Note: According to our answering guidelines we have to solve only one question (if multiple…

Q: Given g (x) = - 3 ( x - 4 )2 - 1, what is the parent function, f ( x ), of g ( x )?

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Q: If f(x) = x +9 and g(x) = -9, %3D (a) f(g(x)) = (b) g(ƒ(x)) (c) Thus g(x) is called an function of…

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Q: Consider the functions f(x) and g(x), for which f(0) = 3, g(0) = 5, f'(0) = 7, and g' (0) = -2. f(x)…

A: We have,  f0=3, g0=5, f'(0)=7 and g'(0)=-2 To evaluate : The value of h'(0) if hx = fxgx

Q: Suppose that f and g are functions that are differentiable at x = 12 and that f(12) = 4, f ' (12) =…

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Q: Suppose that g is a function that is differentiable at x = 4 and that g(4) = -2 and g' (4) = 1. Find…

A: We are asked to find the value of h'(4)

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

A: Given: h(x)=x2+13 To find: The composition of two function. That is h(x)=f(x)∘g(x)

Q: find functions f and g so that f ∘ g = H.

A: A function defines a relationship between two sets, where one set is dependent on other set. Any…

Q: If f(x) = x +2 and x = -3, then slop function is

A: Given f(x)= x+(9/x) and x=-3. We need to find the slope function.

Q: If y = g(u) = u2 / (1-2u) and u = h(x) = x +5, determine the composite functions  (a). g(h(x))…

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Q: For any function  y = f(x),  the difference quotient is defined as  f(a + h) − f(a) h. Our…

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Q: If f(x) is a concave function such that f(x) ≥ 0 for all x then g(x) = ((f(x))1/2 is a concave…

A: We have to evaluate that, '' If f(x) is a concave function such that f(x)≥0 for all x then…

Q: If f(x) : = x + 9 and h(x) = 2x – 4, find a function g such that g of = h. g(x) =

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Q: Suppose f is a one-to-one differentiable function and its inverse f-1 is also differentiable. If…

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Q: If f(x)= x+9 and g(x)= x−9, (a) f(g(x)) = (b) g(f(x))= (c) Thus g(x) is called an…

A: f(g(x) ) = x-9+9 = xf(g(x)) = x

Q: If f(x) = x + 3 and g(x) = x – 3, (a) f(g(x)) : (b) g(f(x)) = (c) Thus g(x) is called an function of…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: If f(x) = x + 6 and g(x) = -6, %3D (a) f(g(x)) = (b) g(f(x)) = (c) Thus, g and f are functions.

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Q: If f(x) = x + 8 and g(æ) = x – 8, %3D (a) f(g(x)) = (b) g(f(x)) = (c) Thus g(x) is called an…

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Q: Suppose f(x) and g(x) are two functions such that: • f(3)=1 • g(3)=1 • f(3)=5 • g'(3)=7 What is…

A: we know that uv' = u'v+v'u                   product chain rule of differentiation

Q: Find and simplify the difference quotient [f(x + h) - f(x)]/h, h ≠ 0 for the given function : f(x) =…

A: Here given function as fx=6 thus  fx+h=6

Q: For functions f and g, if f and g are both even functions, then f + g is even.

A: For _____ functions f and g, if f and g are both even functions, then f+g is even

Q: The function h(x)= (x+4)^5 can be expressed in the form f(g(x)) where f(x)= x^5, and g(x) is defined…

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Q: If f(g(x)) and g( f(x)) both equal x, then the function g is the ________ function of the function f

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

A: Let f(x)=x+5 for x<-1               =cx for -1≤x≤2                =x+6 for x>2 To find the…

Q: Suppose that the selling price p of an item for the quantity x sold is given by the function p=-1/5…

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Q: 2. A size 36 shoe in France is size 3.5 in England. A function that converts shoe sizes 3x-94 in…

A: Consider the function that converts shoes size in France to those in England is  g(x)=3x−944 The…

Q: If f(x) is a twice differentiable function with f(0) = 3, f(2) = 3, f' (2) = 4, Then æ f" (x)dæ =

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Q: Find functions f and g such that h(x) = f(g(x)), when h(x) = (9x³ – 5x)³ – (9x³ – 5x)² + 11.

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Q: If f(x) = x +1 and g(x) = x – 1, (a) f(g(x)) = (b) 9(f(x)) = (c) Thus g(x) is called an function of…

A: Given that fx=x+1 and gx=x-1 fgx is calculated by applying g function first and f function later to…

Q: If f(x) = z+6 and g(z) z- 6, (a) f(9(x)) = (b) g(f(x)) (c) Thus g(z) is called an function of f(z)

A: f(x)=x+6 g(x)=x-6

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

A: To express  function h(x) = (x2 + 2x - 1)4 as a composition of two functions f and g so that h(x) =…

Q: Evaluate the piecewise-defined function. f(x) =    x − 4   if  x < 1 x2   if  x ≥ 1…

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Q: find and simplify f (a +h) -f (a) / h     (h is equal/not equal to 0) for function  F(x) =…

A: Consider the provided question,

Q: Find the following for the function f(x) 3x +3x- 4. (a) f(0) (e) -fx) (b) f(2) () f(x+2) (c) f(- 2)…

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Q: In the following problem, show that f(x) and g(x) are functions by showing that f(g(x)) =x and…

A: Firstly, we calculate f(g(x)) by replacing x by g(x) in f(x) and g(f(x)) by replacing x by f(x) in…