The first divided difference  of f with respect to xi   and  xi+1 is defined by    Select one: True False

Q: Find f such that f′(x)=6x−7​, f(8)=0.

A:

Q: Find the difference quotient.  f(x)=cuberoot of x (f(x+h)-f(x)/h)=((cuberoot of x+h - cuberoot of…

A:

Q: Show that if f (2) = −2 and f'(x) ≥ 5 forx > 2, then f (4) ≥ 8.

A: Given that f (2) = −2 and f'(x) ≥ 5. And also, f(4) ≥ 8.

Q: Suppose that f(x) = 9eª - exº. Find f'(3). f'(3) = |

A: The given function is  f(x) = 9ex - exe . Find f'(3).

Q: Let f(x) = 5z - 6 and g(x) = 2x2 + 8x. After simplifying, %3D (f + g)(x) =

A:

Q: f-(5) = and (f( – 11))

A:

Q: Show that if f (2) = 5 and f' (x) ≥ 10 for x > 2, then f (x) ≥ 10x − 15 for all x > 2.

A: given, f (2) = 5 and f' (x) ≥ 10 for x > 2, To prove- f (x) ≥ 10x − 15 for all x > 2.

Q: Suppose that f(x) = 6x¬4 + 7x-2. Evaluate each of the following: f' (4) = f'(-3) =

A: Given,

Q: If f(x) = x2 - 4 and g(x) = √(x2 - 4), then (f ∘ g)(x) = -x2 and (f ∘ g)(5) = -25.Determine whether…

A: Now, Therefore

Q: A. Identify whether the followin 1. f(x)5x +3 2. f(x)- 5x - 3 3. f(x)x2 - 5

A: Given; 1) f(x)=5x+3 2) f(x)=-5x-3 3) f(x)= x2-5. Repost the next parts.

Q: If f is one-to-one and f( – 15) = 1, then || f-1(1) = and (f( – 15))¯ ||

A: The objective is to to find the required values

Q: Evaluate f(x)=2x+8whenx+-2,x=0, and x=5   when x= -2,f(x)=_____ when x =0,f(x)=_____ when…

A: Consider the provided function, fx=2x+8 Evaluate the provided function. x=-2,x=0 and x=5. Now, find…

Q: Let f(x) = 7-5x and g(x)- 2x-3, Find f(2)

A: Given: fx=7-5x  and gx=2x-3

Q: Find the interval on which f is concave up and Find the interval on which f is concave down. Enter…

A: If F"(x)>0 then F(x) will be concave upIf F"(x)<0 then F(x) will be concave down.

Q: Is f (x) = x2 + 2 one-to-one? If not, describe a domain on which it is one-to-one.

A: Given that the function is f (x) = x2 + 2   f(2)=22+2=6 f(-2)=(-2)2+2=6 So, f(2)=f(-2) So for two…

Q: Suppose that f(x) = 2x4 + 9x2. Evaluate each of the following: f'(1) = f'(-3) =

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: What domain restriction will ensure that f (x) = - 2x 2 + 3 has an inverse?

A: Given that                f(x) = -2x2 + 3 Let   y = f(x) = -2x2 + 3

Q: Let f(x) = 7-5x and g(x)- 2x-3, Find g(2.5)

A:

Q: Suppose that f(x) = 6x¬4 + 7x-2. Evaluate each of the following: f'(4) = f'(-3) =

A:

Q: evaluate f(-3), f(-2), f(-1), and f(0). f(x) ={-2x2 + 6    if x -1}

A:

Q: If F(x) = f(g(x)), where f(-5) = 9, f'(-= 7, f'(4) = 2, g(4) = -5, and g'(4) = 4, find F'(4). %3D…

A:

Q: Find f such that f'(x) = 8x + 9x-2 and f(0) =5. %3D f(x) =| %3D

A: Concept : if f'(x) is known for finding f(x) we need to integrate f'(x) with respective x…

Q: Let f(x)=3x+3 and g(x)=4x^2+4x After simplifying, (f∘g)(x)=

A:

Q: Use synthetic substitution to find f(2) and f(- 1) for each function f(x) x ^ 6 - 2x ^ 5 + x ^ 4 + x…

A:

Q: f(x) =    4x + 7      1< or = x < or = 2                 4x2 - 1      2 < x < or = 4  determine…

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Q: Given f(x)=-9x+3 and g(x)=x', find (fogXx) Given f(x)=2x-5 and g(x)=x+2, find (fogXx) Given f(x)=x…

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Q: If f is one-to-one and f(- 12) = 11, then %3D f-'(11) = and (f( – 12))- =

A: The function f is one-to-one and f(-12)=11

Q: Use f(x) = 2x - 8 and g(x) = 4-x´ to evaluate fAg(-1)). %3D Find f (g (x)) for f (x) = 7x + 7 and…

A:

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

A:

Q: Suppose that f (x) = 8x² – 2x + 5. Evaluate each of the following: f'(9) = f'(-11) =

A: Given,            fx=8x2-2x+5

Q: Suppose that 3 <f"(x) < 5 for all values of x. Show that 18 < f(8) – f(2) < 30.

A:

Q: Let  f(x) =    7x − 2,     x ≤ −5 −x2, x > −5.  Find  f(−1), f(−5), and f(−6).

A:

Q: Evaluate  f '(3). Also, find the two-point forward difference, two-point backward diffrence and…

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Q: Determine f(2), f(-1), f(1/2), and f(-2/3) f(x) = 3x^3 - 5x^2 +2x - 1

A:

Q: If f is one-to-one and f( – 9) = 8, then f-'(8) = and (f( – 9))-

A: The relation f is one-to-one and f(-9) = 8

Q: Find f is f "(x) = 24x2 + 2x +10, f(1) = -7, f'(1) = -2. f(x) =

A: to find the value of f we will integrate the derivative of function given to us  f "(x) = 24x2 + 2x…

Q: Suppose that F(x) = f(g(x)) and g(3) = 6, g' (3) = 4, f'(3) = 4, and f'(6) = 7. Find F'(3). F'(3) =…

A: We have to find derivative at that point

Q: Let f(x) = 11x + 2r and g(x) = -7x- 3r + 4. Find (f+g)(x) and (f -g)(x). Then evaluate f+g and f-g…

A: Given,          fx=11x+2x2  and  gx=-7x-3x2+4

Q: Suppose that F(x) = f(g(x)), g(3) = 6, g'(3) = 4, f'(3) = 2 and f'(6) = 7, find F'(3). mee, UPSI

A:

Q: Suppose that F() = f(g(x)) and g(3) = 6, g'(3) = 4, f'(3) = 4, and f'(6) = 7. Find F' %3D F'(3):

A:

Q: If f is one-to-one and f( – 15) = 11, then f-'(11) - 1 and (f( – 15))

A: Given: f is one-to-one and f(-15)= 11.

Q: If f is one-to-one and f(8) = 9, then f-'(9) = Preview 1 and (f(8)) Preview

A: f is one to one function, it means every x can give unique value of f(x). So f(8) = 9 Then , f-1(9)…

Q: Suppose f''(x) = 42x- 20, f'(- 1) = 47, and f(- 1) -31. %3D Then f(x)

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Evaluate f(x)=5x^4+5x^3+4x^2-2 using synthetic substition to find f(-3). Please show work.

A: Given, f(x)=5x4+5x3+4x2-2 To find f(-3)

Q: Given the function f(x)=−9 x−7, find f(6).       -51     6     -47     -61     33

A: Given, f(x)=−9 x−7-----(1) Replacing x with 6 in equ(1), we get

Q: Let f(x) = 7-5x and g(x)- 2x-3, Find g(1.5)

A: Given that: Here the equation of g (x) is not clear so we take g (x) =2x-3 fx=7-5x,  gx=2x-3

Q: Use synthetic substitution to find f(2) and f(- 1) for each function. f(x) = x ^ 6 - 2x ^ 5 + x ^ 4…

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Q: Suppose that f(x) = 4x 4 + 3x 2. Evaluate each of the following: f'(2) = f'(-1) = %3D

A:

Q: Let f(x) = 7-5x and g(x)- 2x-3, Find f(-1)

A: Given that, fx=7-5x       ...(1)gx=2x-3      ...(2)

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.