(a) Show that the function f : N→Z+ defined by f(n) = n! is not O(n). (b) The function g : R+ + R+ defined by g(x) = r +5! + (r +2 +1) log r is big-O of which one of the following functions? (i) log z (ii) 5! (iii) x (iv) r* (r) z* log r°. Just pick the correct answer. No explanation is required (Hint: Use the relevant theorems from slides/textbook)

Q: Define functions f: {0,1,2} → R+ and g: R+R by f(x) = 4x and g(x) = log2 (x). Write down the ordered…

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Q: Which of the following satisfies the statement f(x) is O(g(x)) when x5log(x+1) f(x) = +16x²? -5x3…

A: Given data:- fx=x5logx+1-5x3-2x33+16x2

Q: find the inverse of the given function by using the “undoing process,” and then verify that ( f ᵒ f…

A: fx=25x+13

Q: The equation for an exponential function is r(x) = 4 · (0.75)x – 9. Which statement correctly…

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Q: Suppose f : R → R and g: R+ → R are defined by f(x) = x2 + 1 and g(x) = log x – x². What is go f? O…

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Q: Prove that Log(2) is discontinuous on R, the nonpositive real axis.

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Q: Find the domain of the function f (x) = log12 (x + 5). O a) D : {x\x -5} OeD: {x\x# -5} O d) D :…

A: Domain Set of all input values where f defined

Q: Show that the function f(x) =r³ – x² + 1, x > has an inverse. 3 If g is the inverse of f, find…

A: Part a:   In part a function f(x) is given and show that the function has an inverse for x>2/3.…

Q: Consider the function f(x) = 24x³ + 3x² + 8x + 12. Show that f(x) is 0(x²) by determining a pair of…

A: if we have a function f(n) that represents the running time or space usage of an algorithm as a…

Q: (d) Show that f(n) is O(n) and 2(n²). You must use the definitions from class, and explicitly define…

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Q: Use the functions f (x) = 4x + 1, g (x) = 2x2 h(x) = -x² + 3x – 19 and for questions 18 - 20. бх,…

A: We have to  find

Q: Find a formula for the inverse function. Assume the functions below are defined on domains on which…

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Q: Consider the function f(x) = 24x³ + 3x² + 8x + 12. Show that f(x) is 0 (x-) determining a pair of…

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Q: a. Given f(x) = x² − 3 and g(x) = √x + 3. Find (f o g) (x) and write the · domain of (fog) (x) in…

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Q: (a) Explain why we know ex has an inverse function—let’s call it log x—defined on the strictly…

A: (a) To show that ex has an inverse function defined on strictly positive numbers.

Q: If fx) = r t 1 and g(x) = 8+x logx 1 what is the domain of (fx g)(x)?

A: To find  The domain of (f*g) (x)

Q: 2. Prove that the function: [x₁ X1 ere x = [2 4 12 16 cover. ( Xn f(x) = n X;P P E R is convex. (You…

A: The given function is fx=∑k=1nxkp1p where x=x1,x2,...,xn∈ℝn+. To prove the function is convex. A…

Q: Which of the following functions has a range of all real numbers and a domain of all numbers greater…

A: Domain of a function f(x) includes those values of x, for which the function is defined. Range of a…

Q: Which of the following functions is/are convex? O a. f(x) = x+11| 10 O b. f(x) = -15 e*-x¹0 O c.…

A: We will use the following theorem that iff''(x)≥0  for all x in domain R then f(x) is…

Q: (ii) A logf(x) = log[1 + E Af(z) f(z)

A:

Q: Let (x) be the sum of the natural logarithms of all the primes not exceeding x. Prove that (x) ≤ (x)…

A: θx be a sum of the all-natural logarithm of all primes not exceeding x. Prove That: θx≤πxlogx