4. Consider the functions f, g, h, k: N→ N given by f(n) = 2 · n+1, g(n) = n² +1, h(n) = 2 · n² +3, and k(n) = 2 (2.n. (n+1) + 1). (a) Show that fog = h. (b) Show that go f = k. (c) Is h = k? (d) Is the composition of functions a commutative operation?

Q: is continuous at x=3, f (-1) =6 ? + a, x # 3 3b, x 3 ontinuous at x=2? - x > 0

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Q: 25. For the function f(x) = 45x3 - 3x5, determine the interval(s) for which f(x) decreases. O (3, 3)…

A: We will solve this question by  differentiating f(x) and then finding the intervals for which the…

Q: 2x C1. What is the asymptotic behaviour for the function f(x) f(x) = 4-z? Ox→ 4, y →∞ Ox→ 4, y →→∞;…

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Q: The Domain of ƒ(x) = V1- x is

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Q: A = 0 0 0 1 1 1 0 01

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Q: 6. Give four non-trivial functions f(x), g(x), h(x) and j(x) such that Vx2 – 1+5 - (f ogohoj)(x) = V…

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Q: The fixed point/s of the function g(x) = In(e²* – 3e* +3) + x on [0,1] is / are: Select one: O a.…

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Q: 18. Which of the following functions has a graph that opens upward? A. f (x) = (x – 7)² – 3 B. f (x)…

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Q: 3. Let h(x) = (f og)(x). Given f(x) = 3x2 +5 and g(x) = Vx – 3. a. Evaluate h(4). b. Determine fx).

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Q: Consider these functions. 1) Evaluate (f + g)(2). f(x) = 3x² – 5 g(x) = Vx - 2 A) -1 B) 0 C) 3 D) 7…

A: we have the given functions  f(x)=3x2-5 g(x)=x-2 1) (f+g)(2)=f(2)+g(2)…

Q: 3. Determine the x interval(s) on which the function is increasing.

A: From the given Figure, it is observed that the graph of function has local maximum at x=-4  and…

Q: f(x+h)-f(x) 2. Evaluate h If a. G) f(Vx) b.

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Q: 1. Let f(x) = x² + 1. %3D (a) Compute f(0), f(-1), f(1/2), and f(/2). (b) For what values of x is it…

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Q: O D. 2x + 2x+4 Find f(-x) when f(x) = 2x-2x+4. OA. O A. 2 +2x-4 O B. -2x +2x +4 OC. -2x + 2x-4 O O O

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Q: for t < -2 t+ 6 f(t) = for -1< t < 2 t2 -- t \3t - 2 for t 2 2

A: Given- ft=t2           for t&lt;-2t+6t2-t     for  -1&lt;t&lt;23t-2      for          t≥2   To Find-…

Q: 26. Let f (x) = vx - 1 and g(x) = x² – 4. A. Find (fog)(x) and (gof)(x). B. Find all real values of…

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Q: Fxy(x, y) is a monotonic and non-decreasing function of both x and y.

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Q: L. nft 7r 2x+1 1 4) f(x) = 2 I- 3 < 1 f(1)= f(-2)= f(6)=

A: The given expression is:

Q: ain of f+g, f-g, fg and

A: As per the bartleby guidelines for more than three parts only three has to be solved. Please upload…

Q: 10. Let f(z) = 4z7z²+3z +1 and g(z) = 4z7. Show that f(z) - g(z)| < |g(z)| for |z| = 1.

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Q: Write the functions f(x) = Σ 33n+1 and g(x) = Σ – n=0 n=0 24n+2 n! in terms of familiar functions.

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Q: 1. Let f(x) = 3x + 1, g(x) = 7 – 2x, and h(x) = x² – 4.x + 5. Find the following: a) (f + g)(2) b)…

A: 1. Given, f(x)=3x+1g(x)=7-2xh(x)=x2-4x+5

Q: 1. Let f(x) = 12 + 22 + 32 + .+x². Show f(x) is 0(x³).

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Q: Let f(t) = 2t² for -4 < t <4 and extend periodically. Compute: f(1) = f(5) = f(-4.5) = f(-8)= f(12)…

A: Periodic function: A function is said to be periodic with period T if f(x+T)=f(x).

Q: b) h(t)=2|t|+1 O odd function Even function Neither odd nor even function

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Q: 7. Modify B(3) to construct a C* function C(2) which satisfies C(2) = 0 if z S 0.. a. b. C(z) = 1 if…

A: please see the next step for solution

Q: 6. Where are the following functions di: x+2 a) f(x) = %3D V(x+2)x

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Q: 3. (10 points) Determine the value of C such that if r +0 f(r) := V16 + 3x – 4 if r = 0 will be a…

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Q: 2. State why the function f(z) = 2z²-3-ze²+e-² is entire.

A: Introduction: Every complex valued function corresponds to a power series. The convergence of power…