The functions f and g are defined as f(x) = 4x+7 and g(x) = 4-3x. f a) Find the domain of f, g, f+g, f-g, fg, ff, and b) Find (f+ g)(x), (f-g)(x), (fg)(x). (ff)(x), (x), and (x). a) The domain of f is. (Type your answer in interval notation.)

Q: Determine the domain of the function f (x, y) In(3-y) 4- x2 – y2°

A: Given function is f(x,y)=ln(3-y)4-x2-y2 Domain is the set of values for which the function is real…

Q: Let f(x)=x2+2x-1 and g(x)=2x-4. Find 3f(x)-2g(x)

A: Given fx=x2+2x-1 & gx=2x-4 To find 3f(x)-2g(x):

Q: Find The value of K, to Continue The function X-2 f(x)= 4-JI4+X メ+23 - %3D メ=2

A:

Q: Given that f(x) = x² + 6x – 40 and g(x) = x +10, find f(x) + g(æ) and - express the result in…

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Q: 8. Given f(x) = -4x5-3x3 + 4x² -7, use synthetic substitution to find f(-3). %3D

A:

Q: Find bn if the function f(x)=x^2.

A: bn-fx=x2 Fourier series of                     fx=x2   is                     fx=902+∑n=1∞an…

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

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Q: find domain of f(x)=-5x+2

A: Recall the following fact.

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: k(x)=−73x−416k(x)=-73x-416 intersects the line f(x)=−25x+4720f(x)=-25x+4720

A: When two lines are intersecting at a point means , that point is common for both lines. By using…

Q: Find f + g, f - g, fg, and f/g and their domains. f(x) = x2 + 2x,    g(x) = 3x2 - 1

A: Given functions are fx=x2+2x,gx=3x2-1. f+g=x2+2x+3x2-1=4x2+2x-1 Domain of f + g is -∞,∞.

Q: The Domain of ƒ(x) = V1- x is

A:

Q: Let f(x) = square root 17 - 5x, g(x) = x2 + 4x -3. Find the domain of F

A: Given,          The two functions are fx=17-5x and gx=x2+4x-3.

Q: Find gof. f(x)=x², g(x) =x -4

A:

Q: If f(x)=3x2-2x+4, Find f'(x) ALGEBRAICALLY

A: fx=3x2-2x+4ddxxn=nxn-1

Q: b. f(x) = x - 3 x² – 9 2-

A: The given function is,   f(x)=x-3x2-9

Q: x5-3x-2-7x c) iii) f"(x) for f(x) = %3D

A:

Q: The domain of f(x)=y=. x-1 x+2 is

A:

Q: If f(x) = - 2x + ax² +2 and f(2) = 2a, find a. %3D 2.

A: A function is a relation connecting two variables, in such a way that one  variable varies with the…

Q: السؤال الثاني |4-x Vx-1 Find the domain of y = - 2 3+x| x+5

A: We have to find the domain of y=4-x3+x-2-x-1x+5 For domain x≠-3, x≠-5 and  x-1≥0⇒x≥1 And…

Q: Find the domain of: f(x) = x2 - x + 5

A:

Q: • The domain of f(x) = is 3-x %3D x2 -1

A: Given f(x)=(3-x)/(x^2-1) Domain of f(x) is the all possible value of x such that f(x) exist. Since…

Q: 5x°+7x Differentiate f(x) - using quotient rule. %3D 2x2-4x+5

A:

Q: If f (x) = 5x2 2a + 7 and g (a) = -2x2 + 6x + 3, then f (x) - g (x) = %3D

A: A function defines a relationship between two sets, where one set is dependent on other set. Any…

Q: бх + 6 Determine the domain of f(x)= x²- 6x

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Q: • The domain of f(x) = 3-x is x2 -1 %3D

A:

Q: The functionf(x)=5x−1 f ( x ) = 5 x - 1 is shown on the coordinate plane. Which statement is true?

A: A limit in which f(x) increases or decreases without bound as the value of x approaches an arbitrary…

Q: 3. Find the domain of g(x) = v16-x² and h(x) = Vx² – 16. Express your answer using interval…

A:

Q: Find f(x) =2x2+3x-5, then prove that f'(0) +3f'(-1)=0

A: Givenfx=2x2+3x−5To provef'0 +3f'−1=0

Q: Find the value of c so that the domain of f(x) = √c - x² will be [-5,5].

A: The function f(x)=c-x2 has the domain -5,5

Q: Find f(x) such that f'(x) = 2x4-7x and f(2)=3

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Q: If f(x) = (2x + 1) (x - 3)°, then f'(2) = %3D

A:

Q: Use the function f(x) =3x2-5x,g(x)=6x-4,h(x)=5-x3 find the (gof)(x)

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Q: Find (f-1)' (a)   f(x)  = √( x3 + x2 + x +1 ) , a= 2

A:

Q: Let f(x)= 56-2) (x+1 What is the domain? b find all x-intercepts OFind y-intercept if it exists?

A:

Q: Let f(x) = 7-5x and g(x)- 2x-3, Find g(-K2)

A: Consider the provided function, fx=7-5x  and  gx=2x-3 Find the expression for g-k2.

Q: If f (x) = 3x + 2 and g (x) = x² - x, find the value. %3D 8(-3) =

A: Given query is to find value of g(-3).

Q: Find f such that f'(x)= 7x +7x-2 and f(0)= 8.

A:

Q: Let f(x) = x² + 2x - 1 and g(x) = 2x - 4. Find 3f (x) - 2g(x).

A: Solution of given question is written in below step.

Q: The domain of f(x,y) = /36 – x² – y² is

A: Given: The function in two variables, fx, y=36-x2-y2.

Q: -1- * f(x) = 6v4 + 3x² find f(2) %3D -2-* 3 f(x) = 2x- find f(2)

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Q: 3. Find the value of the function: If f(x) = 3x - 4x2 + 3x +4, find f(-3). %3D f(-3) =

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Q: If f(x) = 3x2 +2x -1, find f(0), f(3), and f(-2).

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Q: The range of f(x)= -/2-x² is %3D [-/2,0] O [0,/2] [-2,2] [2, 0) [0,2]

A:

Q: Differentiate the function. g(x) = x2. - - 4x + 13 g'(x) = %3D

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

Q: The domain of the function f(x, y) = In(-x² -+1) is: 4 x² + 4 x² + y? > 4 1 x² + y2 <4

A: See the attachment

Q: 14-x Vx-1 Find the domain of y | 3+x x+5

A: The given function is: y=4-x3+x-2-x-1x+5

Q: Find the domain of the function f(x) = /x² – 2x – 15 Domain is (-00,-3]U[5,00) O Domain is (-00,…

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Q: a) Determine the domain and range of the function z = 4 - V9 - (x² + y?).

A:

Q: Find f(x) such that f'(x)=2x4 - 4x and f(2) = 3

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.