The functions f and g are both defined on the domain of all real numbers with f(x) = x^3 and g(x) = 5x + 2. (a) Write equations for the functions f ◦ g and g ◦ f. (b) h(x) = (1/5x+2)^3 . What are the domain and range of h? (c) Find an equation for a function, k, so that h is equal to ONE of these compositions: f ◦ k, k ◦ f, g ◦ k, k ◦ g, or f ◦ k ◦ g. Be sure to show how your composition results in h.

Q: Find the domain of the function g(x) =√(x - 2)/(x - 5)

A: We can not have negative number inside the square root. x-2≥0 So, x≥2

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A: According to guidelines in multiple questions are given then to we have to do one question so please…

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A: Given, k(x) = x2 + (2/x) To check Is the point (1, -2) on the graph of the function

Q: Select the function the expression the product of (f * g)(x) = f(x)= -4x and g(x)= 2x-1 divided by…

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Q: If equations for functions f and g are given, describe two ways to find (f – g)(3).

A: f-g3Subtraction of two function:f-gx=fx-gx

Q: Assume that the function f is a one-to-one function.  (a) If f(8) = 6, find f -1 (6) (b) If f…

A: (a) Given that f(8)=6.

Q: The notation f -1 (x) means the reciprocal of f(x).       True or false

A: Given f-1(x) is reciprocal of f(x).

Q: .) What is the range of the function y= x^2 - 6? b.) For the function g(x)= x^2 +3x - 5, what is…

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Q: Simplify the expression 2а? + 9х + 4 x2 + 8x + 16 22 + 2х — 8 2x2 – 5x + 2 - - and give your answer…

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Q: Find the domain of f.  f(x) = x - 4/(x - 8)(x + 8)

A: