10. For f(x) = Zp [x], define N(f) = the number of elements i N(fg) = N(f)N(g). Define y(ƒ). Then Zp[x]f(x). Then Then N(fg) Y(π™) = N(π)™ — N(π)m-1 for any prime À € Z₂[x]. Is this y multiplicative?

Q: let f(x)= X be 1 213 (-√5 < X<√) Y.V Pind P{/X/7/1.5},

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Q: Which radical function has a domain of (xe Rx≤3) and range of (y e RIy2-4)? Oy--√x+3-4 Oy--√x+3+4…

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Q: (B) [11]13'[xlí3= [7]13 : (HINT: first try to bring the equation to the form [x]j3 = [a]13 ).

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Q: Calculate L6 for f(x) = √6x + 3 over [1,3].

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Q: [3, 5]. - Calculate Rg for f(x) = 7 – x over R8

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Q: Let f(r) = In r Find and simplify f"(x).

A: Please refer the attached image for complete solution. THANK YOU.

Q: 11. a. For the function f(x) = (3x+2), let x, =-1, x, =0, x, =1. Construct interpolating polynomial…

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Q: The error will disappear when using f(x)=x* to find the Lagrange interpolating polynomial p(x) if n…

A: Sol

Q: Let f (x) = 2x + 3. Compute R6 and L6 over [0, 3].

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Q: 1. Find the value of c to make the following piecewise function continuous on the the interval (-o,…

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Q: For the function f (x) = + 8, find f-1(x). (r-4)5 O f-1(x) = V8x – 8 + 4 O f-'(x) = /8 (x – 8) + 4…

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Q: G(n) = (d)o(d) is multiplicative function. If p is prime then G(p*), fork >1 equals dịn Select one:…

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Q: 2. In each case, write the function f(z) in the form f(z) = u(x, y) + iv(x, y): z² (a) f(z)=z³+z+1;…

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Q: Suppose f(x) mx(x²-3)4 Evaluate: [5(1)dr (x²-3)$ +C A B 습(2-3)5+C 10

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Q: Calculate M6 for f(x) = √7x on [0,2]

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Q: 1. Let f(x)= x on the interval [-7r, 7T. (a) Compute f42, given by 1/2 -T

A: To compute the L^2 norm of the given function, following the definition of the norm

Q: Let frx) = (x²+2x), and g(4)=(1++) find gof and f.g.

A: Given, fx=x2+2x and gx=1+1x.   The objective is to find g∘f and f∘g.   g∘f is found as follows:…

Q: Determine the domain of the following functions: За — 6 a) a(x) b) b(x) = /5 – x c) c(x) = 3x4 –…

A: We can find the domain of the given functions as below.