Suppose that the functions g and h are defined for all real numbers x as follows. g (x) = x-3 h (x) = 2x2 Write the expressions for (h-g) (x) and (h+g)(x) and evaluate (h - g)(-3). (h - e)(*) = I (h + 3)(*) = | ? (i*e)(-3) = ]

Q: Let f(x) = -x4 - x³ + x2 + x – 4 and find the value. f(-1)

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Q: The range of f(x)=/4-x² is [0,2] O (-00,2] [2,0) O [-2,0] [-2,2]

A: Range :- set of all output values

Q: Express f in standard form. f(x)= 2x^2 + x - 6 f(x)= x^2 + 2x - 4 f(x)= 2x^2 - 4x + 1

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Q: Use the graph of f(x) = x3 + 3x2 - 4 in the figure given to factor x3 + 3x2 - 4.

A: Given function: And the graph:

Q: Find the constant a such that the function is continuous on the entire real line. - [8x², a = ax -…

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Q: Let f(x) =2x^2 -x +1 and let g(x)=x-4. Which Statements would be true , and could you please explain…

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Q: Let f be a function that is positive and differentiable on the entire real number line and let g(x)…

A: Given: f(x) >0 , f is differentiable on the entire real line  and g(x) =ln(f(x)) g is increasing.

Q: Find a rule for g-1(x) if: g(x)=2x-1

A: Given  g(x) = 2x-1 We have to find  g-1(x).

Q: The domain of h(x) 7 - consists of all real numbers except 0 and 3, represented in interval notation…

A: Given function is hx=1x+7x-3. To find domain. Solution: Domain of a function is the value of x for…

Q: 5Find The alue of K, to Continue The function f(x) = X-2 4- Ji4+X X #23 %3D - メ=2

A: (5) Given: f(x)=x-24-14+x:x≠2k:x=2 Suppose the function is continuous at x=2. Then,limx→2f(x)=f(2)…

Q: How to find f-1(x) of f(x)=x2-18x. Can you please give steps as well.

A: The given function is f(x) = x2–18x.Replace f(x) by y as y = x2–18x.Interchange the variables and…

Q: Let f(x): 10-x-² 2x 9 - if x ≤ 4 if x > 4

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Q: Find the domain of the function f(x) = In(4 - x2).

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Q: If f(x)-x2 for all real numbers, what is f-1 for x>4?

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Q: Find all possible (real number) values of p, q, and r, if any, which result in the following…

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Q: Given that |f'(x)| < 1 for all real numbers x, show that If(x1) – f(x2)| < \x1 – x2| for all real…

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Q: The domain of f(x) = 5x + 7 consists of all real numbers, represented in interval notation…

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Q: Let f be a function that is positive and differentiable on the entire real number line and let g(x)…

A: Consider the given information, gx=lnfx First, we differentiate gx for checking gx is increasing or…

Q: What is the domain in interval notation of the function scrt(x-4)/scrt(x-6)

A: Solution:function :- x-4x-6∵we know that the value in the square root can not be…

Q: The domain of g(x) = 3 consists of all real x - 2 numbers except 2, represented in interval notation…

A: Given :          g(x) = 3x-2 To determine :              The domain of g(x) interval notation

Q: Find if f (x) = 3x* – 4x3 has any absolute extreme value/values in (-2,+00).

A: Givenf(x)=3x4-4x3To find Absolute maximum and absolute minimum values.

Q: domain of f(x) = 2 x + 1 is { -2≤ x ≤3}, which integer is NOT in the range?

A: I

Q: x -4x +5 - Prove that: f' x x-2

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Let ƒ( θ) = θ3 - 2 θ + 2.Use the Intermediate Value Theorem to show that ƒ has a zero between -2 and…

A: Intermediate Value Theorem: Let f(x) be a polynomial function then intermediate value theorem states…

Q: Suppose that f( – 4) = 4 and that f'(x) = 4 for all x. Must f(x) = 4 for all x?

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Q: Suppose that the function fis defined for all real numbers as follows. x+10 if -4 <x<4 f(x) = -5-x…

A: We make a table for each piece x -4 -2 0 2 4 y -6 6 10 6 -6 x 4 5 6 y -9 -10 -11

Q: Suppose that a function ƒ(x) has the property that ƒ(x1 x2) = ƒ(x1) + ƒ(x2) for any two positive…

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Q: What are the zeros of f(x) = (x - 5)(x - 4)(x - 2)? O5, -4, 2 O5, -4, -2 O 5, 4, 2 O5, 4, -2

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Q: Check the continuity of |x-5| 2x-10 0, x + 5 f(x) = x = 5 at x = 5.

A: We need to check the continuity of the following function at x=5.                 Right-hand limit:

Q: Suppose that: f(2) = -5, g(2) = 2,  f'(2) = -1, g'(2) = -3 Find h'(2) a: h(x) = 3f(x)-5g(x)…

A: It is given that, f2=-5, g2=2, f'2=-1 and g'2=-3. a) The function hx=3fx-5gx. Then, find h'x and…

Q: The polynomial f(x)3x²-4 is continuous for all real values x. Select one: True False

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Q: Use calculus to find the critical number of f(x)= x4/4 - x3/3 -3x2+10

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Q: Express f in standard notation f(x) = 2x^2 + x - 6 f(x) = x^2 + 2x - 4 f(x) = 1 - 10x - x^2

A: We can use the standard form of parabola in order to solve the given problem.

Q: The domain of g(x) =3/(x - 2)consists of all real numbers except 2,represented in interval notation…

A: To Determine: The domain of g(x) interval notation as (- ∞, 2) ∪________. Given: we have a function…

Q: The function f(x) = 4 for x < 2 and f(x) = 4 for x 2 2 has domain of all the real numbers. To True O…

A: As we know that domain is all the value of input (x-values) for which a function can define. for…

Q: Determine the maximum number of turning points of f. 3) f(x) = -x2(x + 4)3(x2 - 1) %3D

A: Given :  f(x)=-x2(x+4)3(x2-1)   To Find : The maximum number of turning points of f(x).   Note :…

Q: The function f is defined by f:x --> 10-(x-3)² for 2

A: To find: The value of function at . Calculation: Substitute in function.

Q: Give the domain for f(x)= x-1/x^2+x-30 in interval notation

A: See attached file for a step by step explanation to find the required domain.

Q: A quadratic function is given f(x) 2x^2 + x - 6. Express in standard from. Find vertex and x-and y…

A: We compare the given equation with y=ax2+bx+c So, a=2, b=1 , c=-6 At vertex : For x=-0.25 we find…

Q: Suppose that f'(x) = g'(x) for all real numbers. Explain why there is a constant c so that f(x) –…

A: We need to show that why there is a constant c so that f(x)-g(x)=c for all real numbers.

Q: The domain and the rang of the - * function In (x - 2) are

A: the log function is not defined for zero and negative numbers so the value of x-1 should be greater…

Q: Find f1(-2) whenever f(x)= x2+2x-1/ex

A: We are given f(x)= x2+2x-1/ex. Here, we need to find f1(-2) that is nothing but finding f(-2).

Q: Find the maximum value of f(x)=x^3-3x on the set of all real numbers x satisfying x^4+36< (less then…

A: Given: The function fx=x3-3x To find: The maximum value of given function on the set of all real…

Q: 2-If F(x)= -x²+2x -4 and g(x)= 1/(2x+4) find g(f(-1)) ( ".

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Q: ind the domain and range of the function f(x)=square root of 49-x^2 . Express with interval…

A: Given function is y=49-x2

Q: 7. Determine whether the funcion is even, odd, or neither: f(x) = 1+x2

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Q: х Use the Intermediate Value Theorem to show that f (x) 4 has a solution on 2. (-10,-7)

A: The given function is as f(x) = x/2 + 4

Q: Express all real numbers greater than 6 and less than or equal to 7 in interval notation.

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Q: Let x be a real number. Show that 1 [3x] = [x] + | x + - 3 3 ++1+

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.