Consider the function f(x) = 24x³ + 3x² + 8x + 12. Show that f(x) is 0(x²) by determining a pair of witnesses that proves the big-O relation. (Hint: When x > 1, note that x> log₂ x.)

Q: Write down the times tables for: F3[x]/(x² + 1) and Z[i]/(3).

A: We will use basic knowledge of ring theory and/or field theory to answer this question.

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

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A: If a pair of functions fx and gx are of same order, then limx→∞fg=N where N≠0 is a constant.

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A: we have to find the interval on which f(x) = x2 − 2x − 3 is monotonic.

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A: We are given that a bowl contains 10 chips and only one is red. Draw chips from the bowl without…

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A: NOTE: Refresh your page if you can't see any equations. . take x=4

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A: note : As per our company guidelines we are supposed to answer ?️only first 3 sub-parts. Kindly…

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A: Given

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A: Let f(x)=y. Then y=(1-xn)1/n. In order to write the inverse function expression write x in terms of…

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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A:

Q: Show that the function is continuous. f(x) = log2(x2 + 1)

A: Consider function  fx=log2x2+1   x fx -4 4.087 -3 3.322 -2 2.322 -1 1 0 0 1 1 2…

Q: (a) ( (b)( (c) ( (d) ( ) satisfies g(x). ) satisfies g(x). ) satisfies g(-3x). ) satisfies -g(3x).

A:

Q: find the inverse of the function f(x) = 2x +3/x-4

A: Given query is to find the inverse of f(x).

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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…

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Q: Express the function h(x) = 5log(x² + 6) the form fog. If f(x) = 5log(x), find the function g(x)

A: We can find the function g(x) from the given composite function in the below steps.

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

Q: 2 Let f(x)= 3x - 4 and let g(x) = 2x + 1. Find the given value. fig(3)] f[g(3)] = (Type an integer…

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A: We have to find