If f:A->B, where D is a subset of A, and E subset of B. Prove that if      A-f^-1(E) is a subset of f^-1(B-E).

Q: Given f(x) = 2x^3 + 1

A: Given - A function To Find - Its derivative by using difference quotient method

Q: -35 Find s?(s°+4)

A: We will find out the required value.

Q: For each statement, either prove that it is true or come up with a counter example N(ATA) = N(A) ● •…

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Q: f: ℤ675,683 → ℤ821 × ℤ823 satisfies f(x) = (mod821(x), mod823 (x)). You may use: 1=411⋅821− 410⋅823…

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Q: The number of representatives of a political party, N, in a city council depends on the percentage…

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Q: COSZ 2) if Res(f,x) of the function f(2)=- a) -3/8 b) #-6 2ti c) 1/e d) 8/5 -is

A: To find Resf, π of the function fz=cos zz2 z-π3.

Q: Suppose f(x, y, z) = xyz + 2xy + 2² · Compute the following values -(2,8₁16) - (-2,-8, 16) (1,-1,0)…

A: We have to find functional value.

Q: Using Newton's interpolating polynomial of order 2, namely, bo +b,(x-x)+b,(x-x)(*-x) where x, = 0,…

A: Given:   Newton’s method for polynomial interpolation of order two is given as:…

Q: Suppose that f'(x) = 2x for all x. a) Find f(4) if f(0) = 0. b) Find f(4) if f(2)= -1. c) Find f(4)…

A: Given f'( x ) = 2x

Q: -2 Suppose f(x) = f(x) dx Evaluate: A - In (2) B - 4 3 16 D In (2)

A: Solution... Answer is.  Option..(B)

Q: f (n) + g(n) = 0(max(f(n), g(n)))

A: Big Theta notation (Θ) :  f(n) is said to be Θ(g(n)) if there exist positive constants C1 and C2…

Q: Let f(x)=x²- 3 g(x)=Vx+7. Find f(g(2)) 8 О 12 О -12 O O O O

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Q: If B' is of order 2x3 and BA is order 3x4, then A is of the order T

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Q: B) If fx) =-3x² +13 and g(x) =x'+8r-2; find the following. i) (g+f)(x) ii) Ax) - glr) C) 1) If f(x)…

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Q: Describe the long run behavior of f(x) = x* As x → ∞, f(x) → ? As x → 0, f(x) → ?

A: This question is about function behaviour near infinity

Q: Suppose f(x) = f(x) dr Evaluate: A - In (:) 5 B) 36 In D

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Q: 3) a) Find the real and imaginary parts of the following functions: ^) f(2)= ²² +₁ Z-1 2) f(z) = 3z²…

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Q: 4) f(x²+2) lnx dx = a) (+x) Inx--x+c b) (+2x) inx--2x+c c) (x² + 2) lnx--2x+c d) None of the above

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Q: x2 dx is (ax2+4)(x2+9)

A:

Q: consider the function f(2)= x³ +32+1 in the interval [-3,3]; we can say a) f has no zeroes in the…

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Q: Suppose X~N (μ,σ') then X – H - - N (0, 1) o2 O True O False

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Q: Q2) If f (x) = x + 5 and g(x) = x² – 3, find the following: %3D 1) f(f(x)) 2) g(f(x)) 3) f(g(x)) 4)…

A: Given that: f(x)=x+5          and    g(x)=x2-3

Q: Find domain of the follaw ing fanctionss (^) f(x)= In-2) (6) 67 F=

A: fx=lnx-2 the log function is defined for only positive real numbers so the value of x-2 should be…

Q: Which of the following is the inverse of f(x)=√√x²-4? f'(x)=√x²-4 ƒ-¹(x)=x-2 Option 1 Option 2…

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Q: 3x'e* (x* +1)* 3e a) -+C 2(x² +1) 3e* b) 2(x² +1) +C x? +3 x +1 3 c) +C .2

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Q: 22. Find f/(x) and simplify 1 -1 a) f(z) 3-52+1 3 b) f(x) 1.8Vc) f(x) = 32

A: Given, functions

Q: Given the graphs of f(x), f'(x) and f"(x). Determine which is which. A 1 is f(æ), 2 is f'(2), 3 is…

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Q: 2 4 4 0 -2 2 3 2 1 -1 1 0 05 -2 1. Let A= and C = Let a = 4 -2 -6 5 and 3 =. Compute the following:…

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Q: Evaluate (go f)'(8) - given that: f (6) = 7. f'(6) f (7) = 8. f'(7) 6. f'(8) 6 f (8) 8, g'(6) 7 g(6)…

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Q: If f(x1..... ,e) =g(6,0) h(x,.. ), then %3D Select one: a. consistent b. efficient C. sufficient d.…

A: sufficient estimator:-An estimator "θ^" is said to be a sufficient estimator for θ if it containsall…

Q: Let f (x) = -2r, de fined on -1, 1], then L (P ) = 2 (n– 1) 2- 4 (n+1) 4 (n – 1) 4 (п-1) 2n2

A: We need to find the lower Riemann sum

Q: 11) f(x) = e5x In x A) 65x X B) e5x (1 + In x) X e5x (1 + 5x In x) X D) 5e5x X

A:

Q: Let F(x) = f(f(æ)) and G(æ) = (F(x))² . You also know that f(9) = 10, f(10) = 3, f'(10) = 4, f'(9) =…

A: F(x)=ffx and Gx=Fx2f(9)=10, f(10)=3, f'(10)=4, f'(9)=6 Note:    Multiple questions are given, we are…