Let f(x) = x' + x + 4 and g(x) = 3x + 2 in Zs[x]. Then, upon dividing f(x) by g(x), we get O The quotient is 4+2x+2x^2 and the remainder is 1 O The quotient is 6 +x + 4x^2 and the remainder is 0 O None of these O The quotient is 1+3x + 3x^2 and the remainder is 1 O O O O

Q: Use algebraic manipulation to prove that (X +Y)(X + Y) = X

A: Given: X+YX+Y=X Now, first we shall simplify left hand side of equation.

Q: a. Let f(x) = (-4x² + 3) (-4x² − 3). - Then f'(x) = b. Let g(x) = 2√√x + 3 x4 +2x² Then g'(x) Hint:…

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Q: Determine a value for m so that h (x) = -1/3 x^3 + nx^2 + 8x – 15 has an inflection point at  x = –…

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Q: of Find (7,- 2) if f(x,y) = 4x² + 7xy - 3y? + 6x - 5y - 2. of (7,- 2) = (Simplify your answer.)

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Q: If f (x) = 3x ^ 4 + 5x ^ 3 + x ^ 2-2 then write f (x) as the product of irreducible terms of Q

A: We have to express f(x) as the product of irreducible terms of Q.

Q: 7. Differentiate f(x) = (3x + x)² in three ways. When you have completed all three parts, show that…

A: Given that, fx=3x+x2

Q: Let f(x) = 2x2 - 1 and g(x)= 1 + x². Find (f o f)(x). O x* +2x² +2 4 O 4x4 – 4x2 + 2 | 4 O 2x* + 4x²…

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Q: Consider the Lagrange polynomial that passes through the 4 data points given by 2 8 y 7 | 151 | 407…

A: We know that L0x is given by  L0x=x-x1x-x2x-x3x0-x1x0-x2x0-x3        1 Here, x0=2,x1=5,x2=7,x3=8,x=4…

Q: If f(x).= x³+3x k is divided by (x +1) and the remainder is 12, then - k = -8. True False

A: Given :fx=x3+3x-k*Remainder theorem; - If a polynomial f(x) is divided by x-a then the remainder is…

Q: Let g(x)=x2+6x        and f(x)=4x       Find each of the following.      a)  g(−1)      b)…

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Q: What is the x=g(x) that will diverge the root of f(x) = x3 + 4x2 - 10?

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Q: lim [x² + 3x – 5]

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Q: Let f(x) = x3 + 5. Explain why f(x) is invertible, then show all steps in the derivation of a…

A: Invertible function and it's inverse.

Q: 4 If f(x) = ln(2x² – 3) then f'(x) =? - 2x a) 2x2 – 3 - 4x b) 2x2 – 3 2x c) 2x2 + 3 -4x 2x2 – 3 -…

A: f(x) = ln(2x² - 3) So, f'(x) = 1/(2x²-3) × (2x²-3)' So, f'(x) = 4x/(2x² - 3) .... Option (b)

Q: Find f(g(-5)), if f(x) = „4 and g(x) = (x+ 4)² O -7/9 O -7/3 O 2/9 O 1051/81

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Q: Find f-1 (x) for f(x) = 7x + 4. O 1-²=-²/x-1/ O f¹(x) = -7x+4 O---- O f-¹(x) = -7 x - 4

A: For finding the inverse of a function replace all x with y and all y with x and then solve for y.

Q: Let f(x) = x³ + x + 4 and g(x) = 2x + 3 in zg[x]. Then, upon dividing f(x) by g(x), we get The…

A: Given that,  fx=x3+x+4g(x)=2x+3 Are in Z5x

Q: -2x+ 1 1. Given f(x) = find f-(x) 3 1+ 2x 2. Given g(x) find g-1(x) 7+x 3. Given h(x) = (x- 2)3 +1…

A: As per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: る(4xナx)(10x2+x2-2

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Q: Show that f(x)= = x³+2x-4 4x²-5 is O(x).

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Q: 2. Find f(g(5)) if f(x) = 2z + 5 and g(x) = 3x2 %3D O f(g(5)) = 675 O f(g(5)) = 155 %3D O f(g(5)) =…

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Q: Find the composition f[g(x)] if: O 2-3u10 (10 - 15x2)5 O f(u) = u5 and g(x) = 2 - 3x² (2-3x²)²…

A: fu=u5 , gx=2-3x2

Q: Let f(x) — За — 1, g(х) 1, g(x) x + 2, and - h(x) 3x + 4. Perform the indicated operation. (Simplify…

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Q: The Complementary Function for (D – 14)?y = 0 is . O None O Yc = (C1 + C,x)e100z O Yc = (C1 +…

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