Find a closed form representation for the function defined recursively by ƒ(1)=4 and f(n)=3f(x)+n.

Q: If f(n) and g(n) are multiplicative functions, and g(n) does not equal 0 for all positive integers…

A: Definition 1 : A function f: ℕ→ℂ is said to be arithmetic function .   Definition 2 : An arithmetic…

Q: Let f(x) = 6x + 12 and g(x) = x² – 4. - Find the domain of the following fur (a) (g - f)(x) domain…

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Q: The function f: RR defined by f(x) = 5x3 + 3x2-x + 7 is O(x). True False

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Q: The domain of the function f(x): 11x+8 is x+4 • R-{-4} 10 • R • R-{8} • R-{11}

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Q: What is the vertex of the following function? f(x) = x² + 4x +3 (-1,4) (-2,-1) (4,3) (-4, 3)

A: Solution : Given that f(x) = x^2 + 4x + 3 For vertex of the given function , f'(x) = 0

Q: Consider the recursively defined function: f(0) = 2 , f(n) = 2f(n-1) +5 where n   is an integer…

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Q: Which recursively defined function will result in f(1) = 10, and f(3) = 18? F f(1) = 10 f(x) = f(x -…

A: first find the equation of f(x)

Q: The nth triangular number is the sum of all the integer numbers from 1 to n. For example, the…

A: Triangular number is sum of all integer number from 1 to n

Q: 9) Evaluate the piecewise function for x = -1 and x = 4. 2x + 1 if x 2 h(-1) = h(4) =

A: To evaluate the piecewise function for x=-1 and x=4.hx=2x+1  if x≤2x2-4  if x>2h-1=?h4=?

Q: The function f(x) = -X-3)2 - 4, will have a shift of 4 units to the left. O True O False

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Q: Find a → evaluation for the function (4n+1) 8¹ogn

A: Solution: f(n) = (4n + 1)8log n        = (4n + 1) (23)log n              [here , we assume base of…

Q: Find the largest possible domain of each of the following function. 2x4 + 5x3 + 14x² + 11x – - 27…

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Q: (4) Let f(x) = xª + 2x³ + 6x² + x – 1. Find, with proof, the number of zeroes of f.

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