5 For each of the following functions, determine its differentiability and find its derivative where it exists. x² 2-x (ii) g(x) = x² + 2x - 3| for x < 1 for x ≥ 1 (i) f(x) = { (iii) f(x) = x sin / (iv) m(x) = { x sin (1) for x 0 for x = 0 0

Q: 4² = 1 16

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Q: Find and simplify f(x)*g(x) f(x)= 3x^2+7x+2 / 3x^2+11x+10 g(x)= x^2-3x+2 / 3x^2-5x-2

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Q: Find the general solution of the system whose augmented matrix is given below. 1 -6 0-1 O O O 0 10…

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Q: Equation Factored Form: Equation Standard Form: X-intercepts: Y-intercept:_ Vertex: 10

A: Graph:-

Q: Which of the following inequalities represents the restrictions on the radical inequality 2z+1> 3?…

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Q: The number, in thousands, of bacteria in a petri dish is given by the table below. Time is measured…

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Q: tickets to a play cost $4 in advance and $5 at the door. the theatre club president wants to raise…

A: The advance cost of a ticket is Ca = $4 The cost of a ticket at the door is Cd = $5 The required…

Q: ४ 225x3 49x

A: To simplify the following expression.225x349x

Q: h(x)= Find f(x) such that h(x) = (fog)(x) and g(x)= 10 1-x' f(x) = 10 1-x¹0 10 4 1+x

A: We can solve this as follows:

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Q: 3. Find a function such that the domain is the set of natural numbers and the output produces the…

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Q: How do I write; The absolute function, shifted to the left 9 units.

A: Given: The absolute value function shifted to the left 9 units. To find the equation of the new…

Q: Solve by the system of equation by elimination or substitution. Show the final answers in 4 decimal…

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Q: Solve the inequality and write the notation 7x+5/3x-5 < 5

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Q: Which transformation includes a reflection of f(x) = (x − 1)² + 1 over the x-axis? O f'(x) = (2x −…

A: f(X) = (x-1)2+1

Q: Consider the following data set. 1 2 X Y (a) Plot the data. 2.4 2 3 2 1.4 1 4 1.2 2 5 1.1 4 3 2 2

A: Given Table:- x 1 2 3 4 5 y 2.4 2 1.4 1.2 1.1

Q: If (log1097)/(log108) = logganswer, then what is the answer? answer= i

A: Using logarithmic properties

Q: Let W denote the set of English words. For u, v E W, declare u~ v provided that u, v have the same…

A:

Q: Give the result of applying the row operation R₁ R3 to the given matrix. [(333) -4 2 5 -2 -5 3 -3 2…

A: The solution is given below

Q: Simplify 3 over 3/7

A: Topic- simplification we are given 3 over 3/7 which can be written as 33/7

Q: 11ab 19 The operation "*" is defined on by a*b=- for all a,b € R. Which of the following is true…

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Q: Convert the augmented matrix -2 -5 -2 -3 to the equivalent linear system. Use x1 and x2 to enter the…

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Q: The store is selling lemons at $0.51 each. Each lemon yields about 2 tablespoons of juice. How much…

A: we know:- 1 cup =16 table spoons

Q: The polynomial 2x^3-Px^2+Qx-10 is divisible by x-1 and has a remainder of -6 when divided by x+1 1)…

A: We have to find the value of P and Q and solve F(x)=0.

Q: A doctor has found that, over the years, 95% of the babies he has delivered weighed x pounds, where…

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Q: function of has and f(-3) - 6 then f¹ = If an inverse

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Q: Simplify the expression. Assume that all variable expressions repre: 2m n 8 3 24 n 2m 3 21 -M M 010

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Q: Suppose that the function fis defined for all real numbers as follows. -10+x² if -4<x<4 -x+10 if x24…

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Q: 40 Solve algebraically. x + 2y +z = 3 2x - 3y + 2z = -1 x-3y + 2z = 1

A: Note: Since, the student has mentioned to solve question no. 40, so we are solving accordingly to…

Q: Find the equations of any vertical asymptotes for the function below. x²-2x-15 2 x - 4x-21 f(x) =…

A: The solution is given below

Q: Graph the rational function. f(x)= 2x+2 x+4 Start by drawing the vertical and horizontal asymptotes.…

A: Here, the given function is: f(x)=2x+2x+4

Q: Draw the image of quadrilateral ABCD under a translation by 5 units to the right. B -7/-6 -5 -4 -3…

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Q: 59 which graph?h f(x) d ( X-4 if x ≤ 1 -5 if X> 1

A: Given,

Q: Between the ages of 7 and 11 years, a certain boy grows 1.5 inches taller each year. At age 8, he is…

A: solution -  Here it is given that every year boy's height increasing 1.5 inches so it is a constant…

Q: 6 (W° x 5)-1

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Q: What happens to the function f(x) = (x − 1)² + 1 when it becomes f'(x) = ½ ((x − 1)² + 1)? O It is…

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Q: Find the domain of the function. (Enter your answer using interval notation.) f(t) =  square root…

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Q: Give the result of applying the row operation R3 +7R2 → R3 to the given matrix. 3 5 -1 -3-5 -1 15-5…

A: Given matrix:- 35-1-4-3-5-1-115-5-4

Q: A company’s net sales are ₹ 15,00,000; cost of sales is ₹ 10,00,000 and indirect expenses are ₹…

A: Given: Company's net sales=₹ 15,00,000Cost of sales =₹ 10,00,000Indirect expenses= ₹ 3,00,000

Q: Find the matrix A of the rotation about the z-axis through an angle of counterclockwise as viewed…

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Q: Solve the system using the method of your choice. 5x-3y=0 25x+6y=7 Select the correct choice below…

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Q: T+9/2= 7t-6/14

A: Given query is to find the value of T.

Q: Evaluate. Write your answers as fractions. 5^3/2 = ? -(1/3)^2 = ?

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Q: f(x) = 6-5x+x 9+8x+7x² Find the horizontal asymptote(s). Select the correct choice below and, if…

A: To find out the horizontal asymptotes.

Q: For the piecewise function, find the values h(-8), h(-2), h(3), and h(5). -2x-15, for x < -5 h(x) =…

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Q: f(x) = x = -10 8x² + 3x - 5

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Q: Graph each inequality. y≤2|x-1|

A: As per the instruction, we will be answering the first question. The graph will be the following.

Q: f(x) = 7x 3 - 5x The function is oddlever because f(-x) = f(x) f(-x) = -f(

A:

Q: Solution for f H and K are two subgroups of a group G, then show that for any a, b ∈ G, either Ha ∩…

A: Let H and K be two subgroups of group G. To show that Ha∩Kb=(H∩K)c , for any a, b ∈ G and for some c…

Q: State the excluded values for x^2+x-3 / x^3-x

A: