If f and f og are one-to-one, does it follow that one-to-one? Justify your answer. is

Q: Given that f(x) =x-1 and g(x)=x-x, find (f+ g)(6), if it exists.

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

A: Given function is : fx=3x9 The given function can be written as : fx=3x-9

Q: 121. If f(x) = a", show that f(ax) = [f(x)]“. Problems 122 and 123 provide definitions for two other…

A: Given:  f(x) = axTo Show:  f(αx) = [f(x)]αProofFirst of all Replace x by αx in the f(x) , so we get…

Q: Label each of the following statements as either true or false. Let g: A ------- B and f: B…

A: g: A ------- B and, f: B --------C  f 0 g is one-to-one

Q: There does not exist an entire function whose value on the positive real axis is e'fidt. Select one:…

A: We have to solve given problem:

Q: 1 if g is the inverse of function f and f(x) = 1+x? prove that g'(x)=1+{g(x)}"

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Q: If f is even, then f' is even.

A: The question is taken from the function in which we have to do that f is even then its derivative is…

Q: The function f: RR defined by f(x) = 5x3 + 3x2-x + 7 is O(x). True False

A:

Q: If f(x) = f' (x) for all æ, then f(x) = = f" (x) for all x. True False

A: f(x) = f'(x) for all x Then f(x) = f"(x)  for all x

Q: Consider the following function. f (x) = In (1 + 2x), a = 5, n = 3, 4.6 < x < 5.4

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Q: The domain of f is the ________ of f −1, and the ________ of f −1 is the range of f

A: Given:

Q: The function f ( x) = (x-1)2-3 is not one-to-one. True O False

A: A function f is one-to-one if every element of the range of f corresponds to exactly one element of…

Q: Which of the following constitute the values of domain of f(x)=

A: domain is the value of x for which function is defined.for exa if function value is f(x)=√x-2 so…

Q: If the domain of the function f is not given, then the set of values of the independent variable for…

A: If the domain of the function f is not given, then the set of values of theindependent variable for…

Q: Compute f'(a) for a = 3. f(x):

A:

Q: Define f, 9: R + Ras (x? if x3 and g(x) = 8x – 1. Flnd f•g and gof.

A: We are given f, g : ℝ→ℝ f(x)={x2  3x-2  1-4xif ififx&lt;-1-1≤x≤3x&gt;3 g(x)=8x-1 to find f∘g and g∘f

Q: if f is one-to-one, f(5)=-4, f'(5)=3, find f-1(-4), (f-1)'(-4), and f (f-1 (2021))?

A: f^(-1) (-4)=5 f^(-1) (-4)=5 because f(5)--4. f'(5)=3. f(5)=-4. (f^(-1))(-4)=0. f(f^(-1)…

Q: Evaluate (f x g)(2), given that f(z) - and g(z) -. 2. de".

A:

Q: Use the definition of "f is O(g)" to show that

A: In this question,  we have to use the definition of big-O( stated in step-2) To prove the followings…

Q: Show that f (x) = x + x -1 is one-to-one on [1, ∞ ), and find the corresponding inverse f-1. What is…

A: Given function is: fx=x+x-1 We have to prove that f is one-to-one. Let f(x) = f(y) Then we get,…

Q: 2. Define the following functions: f(x) = x - 5x + 25 a.

A: From the question, it is clear that the function can take input as any real number, Therefore…

Q: Let k(x)=f(x)g(x)h(x). If f(5)=−9,f′(5)=0,g(5)=−3, g′(5)=9,h(5)=−8, and h′(5)=−4, what is k′(5)?

A: Given, k(x)=f(x)g(x)h(x). If f(5)=−9,f′(5)=0,g(5)=−3, g′(5)=9,h(5)=−8and h′(5)=−4

Q: Determine whether the statement is true or false. If f and g are discontinuous at x = c, then so isf…

A: 1. If f and g are discontinuous at x=c, then so f+g. 2. If fx is continuous at x=c, then so is fx

Q: Given that f is one-to-one and f(2)=1, f'(2)=3, f(3)=2, f'(3)=2, deduce, if possible, (f-1)'(2)

A:

Q: Show that if f is one-to-one then f is strictly monotonous,. it means : f is  either strictly…

A:

Q: Let f (x) = 35x. Determine all x for which f (x) = 27.

A: Given, fx=35x.   The objective is to determine the value of x for which fx=27.   So, the value of x…

Q: Determine F(x) if, for all real x and y, F(x)F(y) – F(xy) = x + y.   Hint:  What could F(1) be?

A: Consider the provided question, We have to find F(x).

Q: Given that f(x) =x+4 and g(x)=x-x, find (f+ g)(-4), if it exists.

A: Given functions - f(x) = x+4g(x) = x2-xLet's first find out (f+g)(x),(f+g)(x) = f(x)+g(x)(f+g)(x) =…

Q: Suppose g(x) = f(x) + k. Identify a value of k that transforms f into g. %3D -4 -2 2 k =

A: We have  g(x) = f(x)+k   ....... (1) we have to find value of k. f(x) and g(x) are the straight…

Q: Which of the following statements below are true for f(x) = - 2(x - 1)(x - 2)(x + 3)(x + 4)? * i) as…

A:

Q: Let f(x) = In(5æ² - 4x + 9) f'(x) =

A:

Q: Let 1 f(x) = x + 15 f (2) = Submit Question

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Q: Let f(x)  = 1- x2/3 . Show that f(-1) = f(1) but there isno number c in  (-1, 1)such that  f'(c) =0…

A:

Q: How many one-to-one functions f:[4] to [6] have 5 not in the rng(f)?

A:

Q: Find the following. Let f(x)= x+1, g(x)= 2x, and h(x)=x-2. a. (h o h) (x) b. (f o g) (x) c. (g o h)…

A:

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: Consider the following piecewise function. x<2 f(x) =- 4*-3, 25x<7 x27 1, (-2x +7, Part A: Evaluate…

A:

Q: Let y = f(x) be the piecewise dehned -x- 1, if x <-2, f(x) = {1, if 2 < x < 2, 1, if x 2. - f(-3) =…

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

Q: Let f={(2,6) (3,8) (4,5)} and g(x)=3x+5 x, if g(x)=26

A: Here we have to find the value of x, where the value of g(x) is 26.   According to the question the…

Q: Which of the following correctly describes the end behavior of f(x) = -x* +2x ? O A. As X → - 0,…

A: Given:- Function f(x)=-x4+2x

Q: Given that the domain of a one-to-one function f is [−3, 5) and the range of f is (−2, ∞), state the…

A: Given,

Q: If f is an odd function and g is an even function, is fg even, odd, or neither even nor odd?

A: Consider that f is an odd function and g is an even function, determine is fg, even, odd or neither…

Q: How many one-to-one functions f: [4] to [6] have 5 not in the range of f?

A:

Q: For functions f and g, if f and g are both even functions, then f + g is even.

A: For _____ functions f and g, if f and g are both even functions, then f+g is even

Q: Compute f' (a) for a = 6. f(x) = 5/x

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Q: Find the domains of defination of each of the following function: Vlog.x-2 0/(x)-

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Q: Is the given statement true or false? Justify your answer. 'If f is even, then f' is even.'

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Q: Find the rule for (f ogoh)(x).

A:

Q: Compute f' (a) for a = 6. 5 f (x) =

A: Differentiating with respect to x, we get

Q: , and evaluate the following Let f(x) = 3" and g(x) : 2. %3D %3D = (0)f2 3. g( – 3) = 4. g( – 1) =…

A: