Question 2 Which of the following statements is true? (A If f(x) is N(g(x)), then g(x) is N(f(x)) B If f(x) is N(g(x)), then g(x) is O(f(x)) © If f(x) is O(g(x), then g(x) is O(f(x)) D If f(x) is O(g(x)), then g(x) is O(f(x))

Q: E [X - E ( X)]2 is Select one: O a. V( X) O b. E ( X) O c.E ( X2) O d. S. D(X)

A:

Q: Construct the inverse matrix (if it exists) for the following matrices: [12 61 (а) А %— 4 2. 1 -2]…

A: We will find out the required solution.

Q: Let f (x) = 2x +2 and g (x) = –3x+1 Find g(f(2)) O -17 O -18 O -35 O 18

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Q: Is g = {(x, y) ∈ [−5, 5] × R : x^2 + y^2 = 25} a function from [−5, 5] to R.

A:

Q: Let f(x) 2x -1 then f(x) is x2+1 O(Vx) O equal to the above O None of these O équal to C1) O equal…

A:

Q: Which linear function is graphed on the grid? 90 80 70 60 50 30 20 10 12 3 4 10 56789 20 30 40 50…

A:

Q: if x is even c. f(x) = x + |x|, g(x) 2 if x is odd

A:

Q: By definition, (f o g)(x) f(g(x)) ♥ So if g(6) = 9 and f(9) 16, then (f o g)(6) %3D

A:

Q: a. Choose the proof that shows f(x) = x1 and g(x) = Vx are inverses of each other below. OA. f(x) =…

A: To Determine: Given both functions are inverse of each other.

Q: The domain of f(x) =/4 – x +V x – 4 is (- 4,4] R – {4} (-00,4] [4,00) None of the above

A: Solution:Given   f(x)=4-x+x-4To find the domain of f(x)

Q: Let f(x) = 2log æ+¹ + x + 1, g(x) = 4x²log (32) + 7x log(x²) + 4x, and h(x) Select all that apply.…

A: note : As per our company guidelines we are supposed to answer ?️only first 3 sub-parts. Kindly…

Q: If g(x) = x, then g1 (x) = x. %3D O True O False

A: For the inverse function just replace the g(x) by x and replace x by g-1(x) in the given function.

Q: #8: Suppose that an = as 8n a₁²2² +2a₂x³ + 3a3x²4 + 4a4x³ + ... (i) Σf(n)x"+2 n=0 (ii) g(n)x+1 We…

A: This is a good exercise in summation and we shall see how to change the indices.

Q: 4. Use the definition of "f(x) is 0(g(x))" to show that 2* + 17 is O(3*).

A:

Q: If Xo and X, are two numbers with Xp< X, then the true one is None of the above A O F(XO ) F(X1) BO…

A: We have to solve given problem:

Q: How would you find g (A) if a) g (x) = 1. b) g (x) = (x + 1)2 . c) g (x) =⌊ (2x + 4)/3⌋ Where A =…

A: Disclaimer:  “Since you have asked multiple questions, we will solve the first question for you. If…

Q: If f(x) = e(n =)*) and g(x) = (In x)², then g(f (x)) is equal to.

A:

Q: Let f (æ) = 2a² + 3a + 5 and g (æ) = 2a². Then which of the following is (are) correct? O f(x) is…

A: Given that fx=2x2+3x+5 and gx=2x2 It is clear that 2x2=2x2 So, 2x2≤2x2+3x And also 2x2≤2x2+3x+5 for…

Q: Let h(x) = -3) Then, h(x) has a zero on (0, o). —1) (ӕ+2)(2+3а) O True False

A:

Q: 5.) Evaluate f(-3) for f(x) = x³ +3x + 17

A: Given  f(x) =x3+3x+17

Q: 9x 9* +3 Let f(x) = evaluate Show that f(x) + f(1-x) = 1 and, hence, 3 (1996) + (1996) + (1996) + (5…

A:

Q: 15. If f(x)=x-1 and g(x)=1/ (x+1) , g(f(1/2)),g(g(2)) and f(f(x)) 02, 3/4, x+2 02, 4/3, x-2 02, 4/3,…

A:

Q: Question 3 Is f(x) = x4n-2 - x4n-4 + x4n-6 + ...+ x² - 1 divisible by g(x) = x4 – 1? %3D

A: Binary operations like addition, multiplication can also be performed between two polynomials. When…

Q: Let S={0,8,10,−9,−2}S={0,8,10,−9,−2}. Find f(S)f(S) in each of the following cases. a) If…

A: If f is a function from A to B and C be any subset of A. Then f(A)={f(y) : y is an element of A}

Q: Let f(x) = 4.x³+ 2x 10 and g(x) = x3. (a) Prove that f(x) is O(g(r)). (b) Prove that 9(x) is…

A:

Q: 1-x if x<0 Let f(x)={ x2+3 if 0<x<4 and g(x)= X-5 7 if x24 Evaluate (fog)(2).

A:

Q: 7. Translate these statements into English, where C(x) is "x is a comedian" and F(x) is "x is funny"…

A: ∃x P(x) means that there exists some x such that P(x) holds P(x)→Q(x) means  P(x) implies Q(x), that…

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.