5 Let f(x) = 4 + 12 cos(7x) and g(x) = 6+3x a. Find the composite function f(g(x)) and give its domain (i.e. the values of x for which the composite function is defined). b. Find the composite function g(f(x)) and give its domain (i.e. the values of x for which the composite function is defined).

Q: A. What is the domain and the range of the inverse function of f (x) = 4[sin(n – 2x) – 1]

A: first we will find inverse function then we will find domain and range

Q: Consider the following functions. f,(x) = cos(2x), f,(x) = 1, f(x) = cos²(x) g(x) = c,f,(x) + c,(x)…

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Q: Find F as a function of x and evaluate it at x = 0, x = π/6, and x = π/2. X force 0 F(x) F(0) F(T)…

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Q: Find two functions f and g such that (fo g)(x) = h(x). (There are many correct answers. Use…

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Q: what is a function that takes the same value as im(z) on  γ(0;1)

A: We are to find out the function that takes the same value as im(z) on γ(0;1)   There are many…

Q: Find f ∘ g ∘ h. f(x) = tan(x),  g(x) = x/x-2, h(x) = x1/3

A: We will find the composite function by working from the rightmost function

Q: 4. Let f(x)= |x| and g(x) = x-3. (a) Determine the formulas for each of the related composite…

A: The composite function is defined as when the output of one function is used as the input of another…

Q: Use the table below to fill in the missing values. Assume f(x) is a one-to-one functi f(x) 7 0 2 3 1…

A: A table is given with a one to one function fx values for some values of x. a) The objective is to…

Q: Use a computer algebra system to compute f(k)(x) for k = 1, 2, 3 for the following functions: (a)…

A: given,        a.  f(x) = cot(x2)b.  x3+1

Q: 4. Find range of the following real functionsf: R R. Should clearly specify the interval. For…

A: Range of the function

Q: Find an expression for the inverse of f(x) = e³x+1. f-¹(x) = 4

A: Topic- functions and inverse functions We are given, f(x)=e3x+1 we know that ln(ex)=x

Q: Let f(x) = cosx²) and g(x) = vx. The (natural) domain of (f • g)(x) is = Cos

A:

Q: Find the largest interval on which f has an inverse. f(x)=1/(1+x 4)

A: Givenf(x) = 11+x4⇒y=11+x4Switch x and yx=11+y4⇒1+y4=1/x⇒y4=1/x −1⇒y=(1/x−1)1/4put…

Q: 1 in the form f o g. If g(x) = (x – 1), find the function f(x). Express the function h(x) x - 1

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Q: of the following power functions cou WI apply). O f(x) = x ³ f (x) = x ³ f(x) = x- f(x) = x-

A: Given query is to find the Indicated power function.

Q: The function h(x)=In(x² +c) is concave up on the interval (-4,4) and concave down on the intervals…

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Q: Verify that f has an inverse and find (ƒ~lY(c). f(x) = 2x + cos x; c=n.

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Q: Let g be the function given by g(x) = x² - 2x³ - 3x. What are all values of a such that g′ (x) =…

A: The given equation of function

Q: The function f(x) = (x + 7)³ is one-to-one. a. Find an equation for f(x), the inverse function. b.…

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