Theorem: Assume that f1(x) is O(g1(x)) and f2(x) is O(g2(x)). Then, (i) (f1 + f2)(x) is O(g(x)) where g(x) = max(lg1(x)l, Ig2(x)l) for all x. (ii) (fjf2)(x) is O(g1(x)g2(x)). Using the theorem above give a big-O estimate for n log(n² + 1) + n² logn

Q: IT X) IS defined as foilows, ina (a) i( – 2), (D) (U), and (C) I(2). x? if x 0 (Simplify your…

A: Since the given function is a piecewise function therefore we need to take care of the branch of the…

Q: 3) Show that (f o g)(x) = (go f)(x) = x. f (x) = 4 – 3x g(x) = (4 – x)

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Q: If f(x) = x* + 7, g(x) = x - 5, h(x) = Va, then fo g(x)= go f(x)= ho g(x)= %3D

A:

Q: Find f(x) and g(x) such that h(x) = (f o g)(x). Let g(x) = 2x + 1. 3 h(x) = /2x+1 f(x) =|

A: topic - functions

Q: Could you explain this in detail?

A:

Q: f(g(h(x)))=

A: Givenf(x)=x4+5, g(x)=x-4 and h(x)=x

Q: L 1. Find (f. g)(x) if f(x) = x²+2x+4 and g(x) = -2. O (f.g)(x)=x³-4x²-8x+8 O (f.g)(x)=x³+4x²+8x-8 O…

A: Find the (f•g)(x)

Q: Find f(x) and g(x) such that h(x) = (f o g)(x) and g(x) = /x +5. h(x) = (Vx +5)* f(x)=

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Q: Find h(x) and g(x) such that f(x) = (h o g)(x). f(x) = V3x +4 Suppose that g(x) = 3x+4. h(x) = %3D

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Q: How do you show that if f(x) is O(x), then f(x)=O(x2)?

A: Here we use the definition of big-O.

Q: What is the end behavior for this equation? f (x) = (x − 6) (x + 1) O As a →→∞, f(x) →→∞, and as a…

A: Given: Now,             limx→∞ f(x)=limx→∞ x-6x+1=limx→∞ x-6·limx→∞ x+1=∞·∞ =∞

Q: 3) 4) Find g(3) for g(x) = √-x5. Find p(-x) for p(x) = x³-√1-x .

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Q: Find f(x) and g(x) such that h(x) = (f o g)(x). Let g(x) = 2x+9. 4 h(x) = V2x +9 f(x) =

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Q: The inverse of the function f (x) = 3 – 2x is x+1

A: Solution of question is written in step2.