Consider the tabular representation of f in the table below to create a table for f-1(x). 2 5 10 14 15 f(x) 12 19 3 12 19 f-1(x)

Q: 3) Show that (f o g)(x) = (go f)(x) = x. f (x) = 4 – 3x g(x) = (4 – x)

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Q: Sketch, on the same coordinate plane, the graphs of f for the given values of c. (Make use of…

A: Given the function f(x)=-x2+c;  c=-5,1,5. We need to sketch the graph Let us sketch for f(x)= -x2-5.…

Q: 5. Sketch the function f(x) x(x - 3)(x – 4)

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Q: The function f (x) is defined below. What is the end behavior of f (x)? f (x) = -10x + 70x 100 as x…

A: We have to find out

Q: In Exercises 13-17, let f(x) = x2 + 4x and g(x) = x + 2. Find each of the following. 13. (f + g)(x)…

A: The given function is fx=x2+4x and  gx=x+2

Q: Let f and g be the functions from the set of integers to the set of integers defined by f (x) = 2x +…

A:

Q: Let f(x) = (x – 8)² + 4, æ > 8. Determine f-'(x). f-'(x) = ||

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Q: 20. Let f(x) = 4x2 – 6 and g(x) = x– 2.(a) Find the composite function ( f og)(x) and simplify. Show…

A: Given,

Q: The function f (x) is defined below. What is the end behavior of f(x)? f (x) = -832x2 + 12x + 4096 +…

A:

Q: The domain of f (x) = -x + 4 is {0, 1, 2, 3}, what is the range? O {0, 1, 2, 3} O {1, 2, 3, 4} O…

A:

Q: f and g

A: The linear equation is Pn=13.125-1.75n.

Q: nsider the tabular representation of f in the table below to create a table f-1(x). 7 11 12 f(x) 4 8…

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Q: 7) Construct a table of values for the function f(x) = x 1 in the restricted domain (0, 0.5, 1, 1.5,…

A: Or

Q: 1. Describe all functions f such that f(r) ar² + bx +c and f(1) = 2 and f(-1) = 6.

A:

Q: In Exercises 27-34, let f(x) = x? – 2x and g(x) = x – 5. Find each of the following. 27. (f + g)(x)…

A: Note: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts…

Q: Let f= {(2,6) (3,8) (4,5) and g(x)=3x+5 f(3)-g(3)

A: It is given that  f= {(2,6) (3,8) (4,5)} From the above x value, determine the g(x). g(2)=3*2+5=11…

Q: 8. Consider the function f 1,2,3,4 1,2,3,4} given by the graph below. f(x) 4 3 2 1 2 3 4 a. Is f…

A: F:{1,2,3,4}->{1,2,3,4}From the given graph it can be said that:F(1) = 3F(2) = 4F(3) = 1F(4) =…

Q: 6. Sketch a graph of some function f(x) where the interval for f(x) > O is [2,5] and [8,).

A:

Q: 25 – 3 Evaluate the domain of the function h(z) = 3 - z2 - i

A: The domain of a complex function f(z), is the values of z for which the function is defined .

Q: Discuss the continuity of the composite function h(x) = f(g(x)).

A: It is given that,  h(x)=f(g(x)) ..................(1) where f(x)=x2and g(x)=x-1

Q: A contour map for a function f is shown. 24 7- 18 12 30 5 -4 -3 -2 2 3 40: Use the contour map to…

A:

Q: Differentiate the function.

A: The given function is ,gx=lna-xa+x the above function can be written as, gx=lna-x-lna+x…

Q: Find the domain of the composite function f-g. 7) f(x) = x + 6, %3D g(x) · X+7

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Q: Find a function f(*) such that f'(*) = 322 + 4 and f (0) = - 1 f(2) = [

A: We have to  find function

Q: Use a graphing utility to graph the function. 3|r| f(x) x + 6 10 -30 -20 -10 10 20 30 -30 -20 -10 10…

A: The given function is f(x)=3xx+6

Q: | What are the features of the function f(x) = ()“ – 1 graphed below? %3D 12 11 10 7 6. 4 3. 2 3 4 5…

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Q: Make a table of values for f(x) = x² - 6 showing function values for x = 4, 6, 8,.. f(x) 4 8 10 12…

A:

Q: Sketch, on the same coordinate plane, the graphs of f for the given values of c. (Make use of…

A: Given, fx=-x2+c

Q: A power representation of the function f(r) = for -1 <a<1 is 1+ %3D

A:

Q: Define functions f, g, and h such that F( x) = 1 /x^2 −1 = ( f x g x h)( x) and the domain of F is…

A:

Q: Make a table of values for f(x) = x2 - 7 showing function values for x = 4, 6, 8,... f(x) 4 8 10 12…

A: Solution: The objective is make the table of values

Q: Discuss the continuity of the composite function h(x) = f(g(x)).                                f(x)…

A:

Q: Write out all functions f: {1,2} –→ {a,b, c} (in two-line notation). How many functions are there?…

A:

Q: Given a one-to-one function f (x) such that f(3) = 6 and f(6) = 1, what is f-'(6)? Do not include…

A:

Q: 3. Let f(x) = and g(x) = x2 – 2 - a) f o g(x) = b) go f(x) =

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Q: The graph of f is shown below. Evaluate "f(x) using geometric formulas only. 4 3 (3, 2) (4, 2) 2…

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Q: Consider functions f : [5] → [9] (a) How many of the functions are injective

A: Given :  f :5→9  Calculate : Number of injective functions.

Q: The table below defines a function f(x). x f(x) -3-14 |-2 -3 0 4 2 16 4 22 -1 What is the value of…

A:

Q: Let's look at the function g (x) = ſ 7t²dt. Use the Fundamental Theorem of Calculus Part 2 to…

A: Given, gx = ∫0x7t2dt  We have to find the gx using the Fundamental Theorem of Calculus.

Q: Consider the function f whose graph is shown below. (a) f(z) 9- -8- 7- 6- 5- 4- 3- 2345 67 89 2+ -3+…

A: Proceed as shown below

Q: Find the domain of the composite function f° g. f(x) = 23, -8 g(x) = x - 7 %3! O {x |x * 0, x * 7, x…

A: In order to find the domain the domain of f o g of x, we need to find the function f o g(x)…

Q: Identify the inner and outer functions in the composition (6x? +7) * Let f(u) represent the outer…

A: given composite function = (6x2 + 7)-6

Q: 33) Use the numerical representation of f(x) below to give a numerical representation of g(x)-f(2x)…

A: To evaluate g(x) at various points using the definition in terms of f(x)

Q: Give an example of a function f : A4 → S6 that is not a homomorphism. Justify your answer

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Q: A contour map for a function f is shown. 16 12 20 5 -4 -3 -2 2 3 40: Use the contour map to estimate…

A:

Q: 2. Let f(x) = 2x + 1 and g(x) = a. Determine the domain and range of both f(x) and g(x).

A: Given:fx=2x+1 , gx=1x-3a.Domain of fx:2x+1≥0       2x≥-1x≥-12x≤12 Domain is (-∞,12]y=2x+1x=12,…

Q: Let f be the function defined by f(x)=x3+x2+x. Let g(x)=f-1(x), where g(3)=1. What is the value of…

A:

Q: Consider the function f : {0, 1, 2,3, 4} → {0, 1, 2, 3, 4} defined by the formula f (x) = (x + 2) %…

A:

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.