Which of the following functions are even? □ y = f(x)g(x) f(x) y = 12g(x) y = f(x) = g(x) y = g(x)¹3 Which of the following functions are odd? y = f(x)g(x) f(x) 12g(x) f(x) = g(x) y = y = y = g(x) ¹3

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A: We recall some basics facts about Euler's function to solve this problem.

Q: 3. Prove that ox + 6x -4X12 is irreducible over Q.

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Q: For the function f(x) = 4² -³ calculate the following function values exactly: f(4) = %3| f(7)

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Q: Let f(x) be the function f(x) 1. Find the following: x + 1 f(11) = f( – 10) | (4) 2 (-) f |

A: Given function is fx=xx+1-1. Put x=11 in the function. f11=1111+1-1=1112-1=-112 Therefore, f11=-112.

Q: Use the tables for functions f and g to evaluate each. f(x) g(x) (f - 9)(6) = f(-5) = -5 -3 4 2 1 -5…

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