! (5) If f(x) Option 1 =.. Option 2 then f(x) is reducible in Z5 [x]. x² + 3 x² +1 x² + 2

Q: . If f(x) = - x and g a) (f + g)(x) = \\+2x (4-x)+(3x+7) = 11 + 2x c) (f. g)(x) = (4-x)-(3x+²7)…

A: We are given the functions and we need to find out the following functions as given in the question.

Q: The set of zeros of f(x) = x³ + 4x² + 4x is (B) {0, -2} (C) {0, 2} (D) {2} (A){-2}

A: find the zeros of the function fx=x3+4x2+4x

Q: Show that f(x)=x5-x3-1 has a zero between 1 and 2.

A:

Q: Verify that the factorization for f (x) = x3 + x2 + 1 over Z2

A: Given that, fx=x3+x2+1. Also ℤ2=0, 1 To verify the factorization for fx over ℤ2.

Q: H.w Exl Let f(x)= 4x+2X+243and go)=3x+3x+3xx +4, where 2. t. f(x),900€75LX] Compute POX) +g (x).and…

A:

Q: f(x) = 8+x 8 - x on [4, 6].

A:

Q: (a) Find the critical values and the corresponding function values. (b) State the intervals on which…

A:

Q: PROB.NO. 4 VERIFY THAT (X - 3 )(X - 21) = (X - 21 )(X - 3) = Xx - 5X + 61 FOR [i 2 0] X =0 30 0 0 4

A: To verify the given expression is followed by matrix X .

Q: Differentiate. f(x) = (x 2 - 2x + 4)ex O ex(x² + 2) O ex(x² + 4x + 2) 3 +x+4 O ex(2x - 2)

A: Given the function fx=x2-2x+4ex

Q: a) f(x) = {(3, –4), (2, 1), (–9,–3)} |

A: We have to find domain and range

Q: Let f(x)= = -2 x²+3x O Only 0 O Only 3 O Only -3 Only 0 and 3 What values of x have to be excluded…

A: given  f(x)=-2x2+3xfor domain  x2+3x≠0

Q: Prove x²(x-y)² =x² -y²

A: Substitute x=y in the given equation Then x2(x-y)2=0 ....... (1) and x2-y2=0 ....... (2)

Q: lim [x² + 3x – 5]

A:

Q: Show that x + 5[x²] is 0(x²).

A: This is a problem of complexity.

Q: Rx) = 3* f(x) = 3* -4 -2 2 4 y y 10 10 5. -4 2 4 2 -5 -5 - 10f - 10 y y 10 10 -4 2 2 4 -4 -2 4 -5 -5…

A:

Q: Let fé)--을(t)6. Eveluate f(-8) %3D f68)= ? %31

A:

Q: Show that Q[x]/⟨x 2 − 2⟩ ≅ Q[x]/⟨x 2 + 4x + 2⟩.

A:

Q: Show that f 1 (3) does not exist.

A: Given : To show f'(3) doesnot exists

Q: 2. Let f: RR by f(x) = -2x + 1. Let A = [2,5] B = [-1,3] C = [−2,3] D = [1, 4]. Find each of the…

A: Here are the solutions:  Note:We have provided the best possible solution for you. Kindly, verify…

Q: If f(x) = f(-3) = f(0) = f(2)= 2x-1 x²+3 for x ≤0 for x>0 " evaluate the following.

A:

Q: Prove that x -2x+2>0 for value of x.

A:

Q: )- (3x* -7х +4

A:

Q: (6) (x)어

A: we have been given f4(x)=(x2+1)2 we have to find the value of f6(x).

Q: 2x+11 1 Consider f dx = x2+x-6 x-2 x+3 then evaluate S(-dx xp(* - 3 x+3

A:

Q: 6. Consider the function f(x)= log₂ (x−1)+1 . Find f¯¹.

A: Given  f(x)=log2(x-1)+1  We have to find f-1

Q: Compute f 3 2 x-5x+6 dx.

A:

Q: 2. Find a polynomial that interpolates (-1,4) and (3,6), then find the value of f(x) at x=0 and x=…

A:

Q: Differentiate. f(x) = In (4x + 1)(x+7)³ (1 - 6x)5

A: The solution is given below:

Q: 2 (x? - х- 6) R (x) X State the domain of the following function : 7(x? + 4 x – 21)

A: Given the function:       Rx=2x2-x-67x2+4x-21 Find the domain of R(x).

Q: Compute f 2x-1 (x-5) (3x+1)(4x-7) -dx.

A:

Q: Let f(x)- 3x-4 and gix)= x² +4x +5. Find f(3) = f(-2)- 9(-3): g(2): flat2): glar2)

A:

Q: ,2,,2 Suppose that f(x, y) = 10x²y² + 6x? + 2y? then find the discriminant of f.

A: We have to find the discriminant from the given function

Q: 4. Prove that f(r) = 4x³ - 8² + 2x + 1 has three real zeros. %3D

A: