Example: Give an example of a function and a value a so that f"(a) = and (a, f (a)) is not an inflection point of f.

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: Give a geometrical interpretation of the function In x

A: To give: Geometric interpretation of the function ln x=∫1xdtt. Concept used: The area under the…

Q: If ƒ and g are real-valued functions, how are the domains of ƒ + g, ƒ - g, ƒg, and ƒ/g related to…

A: Consider that f and g to be a real-valued function then the addition, subtraction, product and…

Q: snip

A: We have, f∘gx=fgx Let us consider, fx=1x ;  gx=x Then we get, f∘gx=fgx=fx=1x

Q: Give an example of Piecewise-Defined Functions?

A: By a piecewise defined function, a function of the form

Q: 1. What is an appropriate domain for the function? Explain how you know.

A: The domain of any function f(x) is the set of all values of x for which the function is defined.

Q: What does it mean if a function f is increasing on an interval?

A: Let the given function be y = f(x) And the interval be I.

Q: Identify a function f that has the given characteristics. f(-5) = f(2) = 0; f'(-1.5) = 0, f '(x) 0…

A:

Q: (1 point) Let f(x) = Find f'(x). 7x² + 2 f'(x) =

A:

Q: The function notation f^-1 (x) mean 1/f(x)

A: Yes this statement is true. And also f-1(x) is inverse of a function. While 1/f(x) is reciprocal of…

Q: Can a function be both even and odd? Explain.

A: To check whether a function can be both even and odd.

Q: EXAMPLE 5 Showing That Two Composite Functions Are Equal If f(x) = 3x – 4 and g(x) : (x + 4), show…

A: fx=3x-4    and gx=13x+4

Q: Find f+g , f-g , ƒ•g, for functions x+1 ) ==", g(x)=-. State the domain of each of these functions.…

A:

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

A:

Q: What is the domain and range of a function in calculus?

A: Domain of a function: All possible x values which a function accepts are called the domain of the…

Q: Our goal is to use function notation to represent the total fuel cost, in terms of the distance (in…

A: Since, you have post multiple question. I am answering first three sub parts. Please post again for…

Q: Give an example of two functions (x) and g(x) such that (f g)(x) does not exist. Explain your…

A: The expression f∘gx can be written as fg(x). The expression f∘gx is calculated by substituting g(x)…

Q: Define the Piecewise-Defined Functions with an example?

A: Definition of Piecewise-Defined functions

Q: Function g:R → R, defined by g(x) =x*+5 is a one-to-one function. True False

A: (7) To check if g:R→R defined by gx=x4+5 is one-to-one function.

Q: Express the function H in the form f(g(x)). Use non-identity functions for f(x) and g(x).…

A:

Q: True or False: If f is an odd and invertible function, then f-1 is an odd function.

A:

Q: If f and g are odd functions, show that the composite function f ∘ g is also odd.

A: It is given that f and g are odd functions.

Q: Using the graph of the function f(x) Fill in the Characteristics

A: The domain of a function is the values of the variable that can be input into the function that…

Q: The function f (x) is defined below. What is the end behavior of f (x)? f(x) = 3x + 54x – 729x – 729…

A:

Q: Determine whether the statement is true or false. If it is false, explain why or give an example…

A: Given: if f is a function, then fax=afx

Q: Let f (x) = e-*x². Use calculus (derivatives) to find the absolute maximum and absolute minimum of f…

A:

Q: Mathematically show that f(x) = 3x³ – x is an odd function.

A: A function f(x) is said to be an odd function when; f(-x)=-f(x) where the sign is reversed but the…

Q: Sketch the graph of a differentiable function f such that f > 0 and f′ < 0 for all real…

A: The function will be differentiable and f > 0, f' < 0

Q: Explain what it means for a function to be (1) and give an example of such a function.

A:

Q: Sketch the graph of the arbitrary function f such that

A: For all values of x < 4, the derivative of the function fx is greater than zero or positive. This…

Q: f(x) is a function,          when,Domain f(x)=rang f(x) then,function f(x)=?

A: As we know the definition of One - One and onto function :- If Domain f(x)= Rangef(x)  Then f(x) is…

Q: Identify a function f that has the given characteristics. f(-3) = f(1) = 0; f'(-1) = 0, f '(x) 0…

A: Given: f-3=f1=0; f'-1=0, f'x<0 for x<-1;  f'x>0 for x>-1

Q: Can a function be both even and odd? Give reasons for your answe

A: We know

Q: Determine the functions domain and range. f(x) = (x - 1)² - 2 %3D O domain: [-2, ∞) range (- 0, 0)…

A: The domain of a function f(x) : The set of values of x for which the function f(x) is defined.…

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: 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: Express the function in the form f. g. (Use non-identity functions for f and g.) F(x) = (3x + x2)4…

A: topic - composite functions

Q: Express the function in the form fo g. (Use non-identity functions for f and g.) G(x) 1 + X {f(x),…

A: Given,G(x)=x1+x3

Q: Sketch the graph of the piecewise defined function: f(x) = 2, x ≤ −1          x − 1, x > −1

A: Given  f(x) = {2,   x≤-1              x-1, x>-1}

Q: Distinguish the Domain in A Function f of Two Variables from Range in A Function f of Two Variables

A: Suppose the function is: f:ℝ2→ℝ2

Q: Give an example of two functions h(x) and g(x), such that (h o g) (x) does not exist. Explain your…

A:

Q: Function g: R → R, defined by g(x) = x* +5 is a one-to-one function. True False

A:

Q: (1 point) Let f(x) Find f' (x). V7x2 + 2 f'(x) =

A: Here we need to calculate the derivative of the given function with respect to x. The entire…

Q: How to find the domain of a Function involving a denominator? f (x)= (x+1)/ (2-x)

A: We have to find the domain of f(x).  For f(x) to be exists  Denominator must be non zero

Q: it a function

A:

Q: Sketch

A:

Q: A function is a rule for which each input is paired with ________ ____ output.

A: We know that a function is a rule for which each input is paired with only one output

Q: Find F as a function of x and evaluate it at x = 2, x = 4, and x = 6. F) - [- Part 1 of 8

A:

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: x7-x 2- Show that the function f(x): odd or even 1+x*

A: When x replace _x then we have same function it is even otherwise odd