(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) which one of the following functions? x5 + 5! + (x4 + x² + 1) log xº is big-O of (i) log xº (ii) 5! (iii): „4 (iv) x5 (v) xª log xº. Just pick the correct answer. No explanation is required (Hint: Use the relevant theorems from slides/textbook)

Q: For any real number b > 1, and any real numbers x True False log, (x - y) = > 0 and y> 0, it must be…

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Q: What is the inverse of the function f(x) -In(5x + 1) – 7? ex – 6 elx + 7). 5 O fx)= elx+7] -4

A: Topic = Functions

Q: 3. If ƒ(x) = log₂(−(x − 6)) and g(x) = √(x + ²) a) Determine the domain of g(x) + f(x) b) Is there a…

A: We want to find domain of g+f

Q: a) x1+2log x = 100.x log x

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Q5. Find z (1) 3 log, 2+log, 25-log, 20 = log (2) logą z + logs (2-3) = log, 10 (3) Inz-10.1285

A: As we know from the logarithmic properties: 1). logbxa=a·logbx  where x,b>0, b≠1 2).…

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A: Given problem:-

Q: 1 prove that there is no branch of the logarithm defined on G =C- {0}

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Q: 2(д-1)(1-и) 9-1)(2-и)и+1 log((q-1)(2—и)и+1) u? > 0 for u > Show that u E - 0, 1], q > 3

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Q: Q3 Identify the restrictions on x and solve for x. log,(6-x) = 2 0 < x < 6, x = 4 0 < x < 2, x=2

A: Identify the restrictions on x and solve for x  logx6-x=2

Q: Let f(x) = ln(x^2 - 1) and g(x) = ln(x+1) + ln(x - 1) a) find the domain of f(x) and g(x) -…

A: The given function are fx=lnx2-1 and gx=lnx+1+lnx-1. (a) The domain of the function ln x is x&gt;0.…

Q: The domain of the logarithmic functiort f(x)=log_(a)x is

A: We find domain of the logarithmic function f(x)= logax.   Where, a &gt; 0 is a constant.

Q: Differentiate with respect to x:* y = log, (x) :() 2+ In x - In x Option 2 Option 3 2 - In x 1+ In x…

A: As per guidelines we can answer only one question at a time so if you need more answers kindly…

Q: 19) Consider the function y = 5 log (z + 12) – 8. Complete the sentence about the graph of the…

A: Given that  Function y = 5log(x+12)-8

Q: #11

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Q: -10 State the range. a. (4, 0) o. [2, 0) c. [4, 0) d. (-0, 0)

A: Definition of the range of the function helps to find the range of the given function. A set that…

Q: 22. Find expressions for f(g(x)) and g(f(x)), and state their domains a) f(x)=√√√x;g(x)=x²-4 f(g(x))…

A: Solution :- The domain of a function is the set of input or argument values for which the function…

Q: 3) Calculate by means of the logarithm: a) x¹+2log x= 100.x log x b) log(x+2)+log(x-7) = 2.log (x-4)…

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Q: 8. If (* = 256 and log (x - y) = 3, calculate the exact values of and y algebraically. Show work for…

A: Given ( 14 )x + y  = 256log4( x - y ) = 3

Q: Where are the following functions continuous? a) f(x) = (2-x)/(x3 -x) b) g(x) = log(x2 -81

A: We have to find the point of continuity of the given function.

Q: (1) and (2). Prove, for each pair of expression (f(n), g(n)) below, whether f(n) is 0, 0, or of…

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Q: Select all of the following that are equivalent to 1, for all natural numbers, n. A. O (1)! В. О B.…

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Q: 7. Given the functions f(x) = log₂ (x-1) and g(x) = log₂ (9-x²), c) Determine (f-g)(x). b) State the…

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Q: log3 [X² 4²³) 7 A) 9 log3 (x) + 8 log3 (y) - log3 (7) C) (9 log3 (x))(8 log3 (y)) - log3 (7) O B) 9…

A: Using Log(xy)=log(x)+log(y) And log(x^a)= a log(x)

Q: af af Әх' ду f(x, y) = 3(x2 + y2) log(x2 + y2), (x, y) ≠ (0, 0) 3x(log(x2 + y2) + 1) Find Əf ах af…

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Q: The function f(x) interval [1, e] at x = Hora lo 0 x is the nat

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Q: IV. odvice veren V. Directions: Use the laws of logarithms to expand the expressions as the sum,…

A: " Since you have posted a question with multiple subparts, we will solve first three subparts for…

Q: The function f(x)=log_(2)x has been transformed, resulting in the function g(x)=log_(2)(x+3)-1…

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Q: Q 1. True/False Tell whether each of the following statements is true or false. Please explain. (a)…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Suppose b is a positive constant greater than 1, and let A, B, and C be defined as follows. log, 3 =…

A: The question is from the topic of Logarithmic

Q: If f(x)=10*+²-5 and g(x)= log(x+5)-2, show that the functions are inverses of one another using…

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