Are there two functions ƒ and g such that ƒ  g = g  ƒ? Give reasons for your answer.

Q: Either prove the following statement is true or provide an example to illustrate it is not true: if…

A: This question can be solved using the concept of even function.

Q: If ƒ and g are functions then ƒUg is s a function.

A: We need to prove that, if f and g are functions, then f ∪ g is a function.

Q: Suppose that f and g are both odd. Which of the following functions are even? Which are odd? y = f…

A:

Q: If f(x) and g(x) are two functions defined by f(x) = √(x + 1) g(x) = | x - 1 |, then what is the…

A: To find f(g(9))

Q: f (x) x + 9 and g() = x - 9,

A: (a)  fgx=fx-9=x-9+9=x (b) gfx=gx+9=x+9-9=x

Q: There can never be two functions f and g, where f ≠ g, for which (f ∘ g)(x) = (g ∘ f)(x).Determine…

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Q: What is the value of f' () if f(x) =? tan x 1 1- 2 Option 1 Option 3 1+ 2 -1 Option 2 Option 4 EIN

A: Recall: ddxf(x)g(x)=g(x)df(x)dx-f(x)dg(x)dxg(x)2 (Quotient Rule ) d(tanx)dx= sec2x

Q: If g(x) is an even function, then f(g(x)) is even. Is this false or true.

A:

Q: Find two functions f and g such that (f . 9)(x) = h(x*). h(x) = x + 6 - | (f(x), g(x))

A: Given (f o g)(x)= h(x) And h(x) = 1/(x+6)

Q: The one-to-one functions g and h are defined as follows. g={(-4, 1), (2, 7), (3, 6), (5, 8), (8, 3)}…

A: answer-1  to find the domain and range of the inverse, just swap the domain and range from the…

Q: 1. If f(x) = x + 5 and g(x) = x – 5, (a) f(g(x)) = (b) g(f(x)) (c) Thus g(x) is called an function…

A: Note: According to our answering guidelines we have to solve only one question (if multiple…

Q: Suppose that f and g are both odd. Which of the following functions are even? Which are odd? y = f…

A: y=f3(x)f is odd function: f(-x)=-f(x)

Q: Find two functions f and g such that ( f ∘ g)(x) = h(x). h(x) = ∛(x2 − 4)

A: Given: hx=x2-43

Q: Find two functions fand g such that h(x) = (f 0 h(x)=√√5x-1 g)(x).

A:

Q: (a) What does it mean if a function f: A B is not surjective?

A:

Q: find the domain and range. of f, g. f + g, and f•g. f(x) = Vx + 1, g(x)= Vx – 1 %3D

A: Given,          fx=x+1 , gx=x-1

Q: Suppose f and g are positive functions. Is the following true or false? Vf,g:N → R f(x) E O(g(x)) =…

A: Big-Θ notation: A function g(n) is in Θ(f(n)) if there exist constants c1, c2, and N such that…

Q: If f and g are the functions whose graphs are shown, let u(x) = f(x)g(x) and v(x) = f(x)/g(x). %3D

A: Given data:   The expression for the first function is u(x)=f(x)g(x). The expression for the second…

Q: Find f°g and the domain of the composite function. f(x) = |x], g(x)=x+3

A:

Q: What describes a true relationship between the f(x) and g(x) over the interval [2,4] 4 f(x) 1 3 7 9.…

A: Follow step 2 .

Q: Which of the following theorems does not require the differentiability of the given function? a.…

A: We can check in which theorem , the condition of differentiability of the given function does not…

Q: Suppose that f (x), g(x), and h(x) are functions such that f (x) is Θ(g(x)) and g(x) is Θ(h(x)).…

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Q: Find two functions f and g such that ( f ∘ g)(x) = h(x).

A: Here h(x)=4(5x+2)2 ...............................(1) It is also given that; f∘g(x)=h(x)

Q: s) Let f(x) 1 and g(x) 4 + 6. - х — 6 Then (fo g)(x) = (go f)(x) =

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Q: Suppose that f and g are both odd. Which of the following functionsare even? Which are odd?(a) y = f…

A:

Q: If f(x)=10sin(x)+3cos(x) , find a function g so that g"(x)=f(x) given that g(0)=0 and g(2)=12 .…

A: Given query is to find g(x).

Q: Prove or disprove. The function f(2) = 2z – 3 – ze? + e=% is not entire.

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: The one-to-one functions g and h are defined as follows. g={(-5, 5), (-4, -1), (1, 7), (7, 8)} h(x)…

A: Given: The one-to-one functions g and h are defined as follows:g=-5,5, -4,-1, 1,7, 7,8hx=3x+10 To…

Q: Suppose that f and g are functions such that (0) = 4, f'(0) = 5, g(0) = –2, gʻ(0) = 3. %3D æf(x)…

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Q: Find functions f and g so that  h(x)=(f•g)(x) for h(x)=1/x^3-7

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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: we define the first difference δf of a function f by δf (x) = f (x + 1) − f (x). Show that for any…

A: Given that the first difference of a function is defined as

Q: If f(x) is a concave function such that f(x) > 0 for all x then g(x) = ((f(x))1/2 is a concave…

A: The given statement is

Q: If f(x) = x + 1 and g(x) = x – 1, – 1, (a) f(g(x)) = (b) g(f(x)) = (c) Thus g(x) is called an…

A: NOTE: Refresh your page if you can't see any equations. . . now for the function f, substitute x-1…

Q: Let g(x) = = X-f(x) S(x) , find g'(1),if f(1) = 4 and f'(1) = 2

A: Given that g(x) = -x-f(x)f(x). We have to find the value of g'(1). Given that f(1) =4 and f'(1) =2.…

Q: Let f(x) and g(x) be two differentiable functions, and define the functions

A:

Q: Let f and g be functions such that f(0)=4, g(0)=6, f′(0)=6, g′(0)=-4, Find h′(0) for the function…

A: First obtain the derivative of h (x).

Q: Suppose that f and g are differentiable functions such that f (0) =2. f'(0) =-5. g (0) =- 3. and…

A:

Q: -- Let the function f(x) have the property that f' (x) = x+1 If g(x) = f(x²) find g' (x). х-5 g'(x)…

A: Simply use the chain rule of derivative .

Q: Give an example of functions f and g such that f ∘ g = g ∘ f and f(x) ≠ g(x).

A: Let fx=ex and gx=lnx. Now, fogx=fgx=flnx=elnx=x gofx=gfx=gex=lnex=xlne                   lnan=nlna…

Q: 3. (a) If f:X→ Y and g: Y→ Z are functions and go f is one-to-one, must g be one-to- one? Justify…

A: Answer is NO  It is not necessary that if g∘f is one one then g must be one . But some time it may…

Q: Function f is defined as follows: f(x) = { (x−2)² +3, x+1 30 2 " 0≤x≤3 3 5

A: This is a problem of real-valued function and Integration of area and inequality.

Q: Functions f and g are defined as follows: f:R - {2} → R, where f(z) = 4 and g: R R, where g(x) =…

A: Two equal functions' condition: 1. domain of f(x) = domain of g(x) 2. f(x) = g(x)   for x ∈ domain

Q: Show that f(x) and g(x) are functions by showing that f(g(x)) =x and g(f(x) = x f(x) = (x-2)^2 g(x)…

A:

Q: If the domain of a function f (x) = x2 +1 is [0, 1], then its range is.. Select one: [0, 1] a. b.…

A: To solve the following problem we use the defination  range of the function

Q: o f(x) f(x) is not a function because when x < 0 f(0) is undefined < 0 is undefined is defined

A: We have to complete the sentence.

Q: Find two functions f and g such that h (x) = (f • g)(x) and f (x)#g (x)# x. h (x) = (x + 1)² f (x) =…

A: Given hx=x+12

Q: 3. (a) If f: X→ Y and g: Y→ Z are functions and go f is one-to-one, must g be one-to- one? Justify…

A: