78. The domain of a one-to-one function f is [0, c ), and its range is [5, * ). State the domain and the range of f.

Q: 2. When can we say that a function is continuous at an interval?

A: We know that when a function does not have any discontinuity, then it is a continuous function. It…

Q: 8х + 7 State the domain of the function f(x) = in interval notation. 9х + 2

A: A detailed solution is given below

Q: Suppose f is a function with property that f(x) ≤ x 2 for all x. Show that  f'(0) = 0.

A: Suppose f is a function with property that f(x) ≤ x2for all x. Showthat f'(0) = 0.

Q: Suppose that f is an odd function; i.e., f(-x)=-f(x) for all x. Suppose that f'(xo) exists. Which of…

A:

Q: 13. Find the end behavior for f(x) =x- 2 A. x- +0, f(x) - +o x--o, f(x) → - B. x +o, f(x) - +0 x--o,…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 3)Verify Rolle's Theorem for the function f(x) = 2x2 + 4 defined over the interval [-6, 6]. Justify…

A: Rolle's theorem is satisfied if : f(x) is continous at given interval. f(x) is differentiable at…

Q: Is the function f : Z→Z defined as f(n)=n^3+2 one-to-one ?

A:

Q: 50. Is the function given by f(x) = 3x - 2 continuous at x = 5? Why or why not?

A: Given: fx=3x-2 Concept Used: Linear function is continuous everywhere.

Q: ) On what interval is f increasing?

A:

Q: Below is the function f(x). 7- to 4 -7 -6 -5 f4 -3 -2 -1 1 2 3 4 5 6 -2 -3 -4 -5 -- =7 Over which…

A: For a given function , f'(X) represents the change in function value over a small interval. So, If f…

Q: Find the extreme and possible points of inflection (if an exist) of f(x) = In x

A: If a function f(x) is given, to find its inflexion or extrema, first find the critical points of the…

Q: 4. List the discontinuities for the function f(x) = cot(* :).

A: First write the given function into Numerator and denominator form and , to find the discontinuity…

Q: [1, 5] th- or f(x) is

A:

Q: 19. Show that f(x) = x² + 1 is not one-to-one, using values of f (not the horizontal line test).

A: To show: The function fx=x2+1 is not one to one. Concept used: The function is one to one is and…

Q: - Show that the function f(x) = secx.cscx odd or even

A:

Q: 13- Given that f(x) is an odd function, classify each of the following as even, odd, or neither .(…

A: The definition of even function is if f(-x)=f(x) and the odd function is f(-x)=-f(x) the odd…

Q: 4. Explain what it means for a function f to be continuous at a point x = c, with a sentence that…

A: Given: We have to explain about function f  to be continuous at a point x=c

Q: Analyze the following graph of f' (x). Õver what interval is f concave down? 2 1 -4 -3 -1 4 -1 -2 -3…

A: Given  The graph of f'x  We have to find the intervals in which f is concave down.

Q: For what value of k will the function f be continuous on (-, ∞)? x2 - 81 if x + -9 f(x) = X + 9 k if…

A:

Q: 71. Is the function given by g(x) = 4x - 6x continuous on R?

A: To check whether the function g(x) is continuous on ℝ. The given function is gx=4x3-6x Also, the…

Q: 13. In the table of signs, interval 0 < x<÷, is the function increasing or decreasing?

A: A function f(x) is decreasing on the interval (a , b)  if f '(x)&lt;0  for every x in (a , b)

Q: 7. If, for all real numbers x, f'(x) 0, which of the following curves could be a part of the graph…

A: For all real numbers xf'(x)&lt;0 ⇒f(x) is decreasing for all real numbers.f"(x)&gt;0 ⇒f(x) is…

Q: 4. Check whether the Mean Value Theorem can be applied to the function f(x) = 4x2 – 8x + 4 defined…

A:

Q: Suppose that (picture) If f is  continuous for all real numbers, then c is equal to:

A:

Q: (b) Use the definition in (a) to compute f'(2) for the function f(x)

A:

Q: 4. Consider the functions g(x) = and . Determine (12)- (}),

A:

Q: 11. What property must f(x) have in order for f'(x) to exist?

A:

Q: 14. Explain why there is no value of k that will make the following function continuous. 5x, if x 3…

A: Given that: f(x)=5x,   if x&lt;-1x+k,    if -1≤x≤32x2  ,   if x&gt;3

Q: Consider the graph of a function f on the interval [0, 4).

A: We have to conclude about local extreme value of f from the graph.

Q: Suppose f(æ) = |x| · x Then f-l(x) = if æ > 0, and f-'(x) = if x < 0.

A: given that fx= x.xfind f-1x for x≥0 and x≤0

Q: What can be said about f (3) if f is continuous andlim f(x) = ½? x→ 3

A: Given that, the function f(x) is continuous and limx→3fx=12. Since, function f(x) is continuous in…

Q: The graph of the function f'(x) of a continuous function f is shown. On what intervals is f concave…

A: It is given that,the graph of the function f'(x) of a continuous function f.  We have to find…

Q: What are the discontinuity and zero of the function f(x) = x^2+8x+7/x+1    Discontinuity at (1,…

A: Given,        fx=x2+8x+7x+1        fx=x+7x+1x+1      Discontinuity at x=1  at f1=x+7=8…

Q: Estimate the one-sided limits for the function below.  f(x)=(11−x)/(x−8)^2

A: Given:

Q: Suppose f is a function with domain [a,b]. If f is an odd function, what can be deduced about a and…

A: According to question f is a function with domain [a, b]  And f is an odd function.

Q: Consider the piecewise function f(x) defined by 6 — 2х if x 4 х? — 16 For which x E R is f(x)…

A: Given function is fx=6-2x                            , if x≤4x-4x+4x-6x2-16    , if x&gt;4

Q: 5. Find three relation from {1, 2} to {6, 7} that are NOT functions.

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: If the graph of a function f(x) is decreasing over the interval (a, b) then which of the following…

A:

Q: Find the discontinuities of the function 2х — 1 - if 2 < x x +1 1 Let G be the function defined by…

A: Given,

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

A:

Q: 9 Determine the domain of the function f(x) 5 - Domain (in interval notation):

A: Solve for the domain

Q: Suppose that a function f whose graph contains no breaks or gaps on (a, c) is increasing on (a, b),…

A: Given, Suppose that a function f whose graph contains no breaks or gaps on (a, c) is increasing on…

Q: 8х + 7 State the domain of the function f(x) in interval notation. 9ж + 2

A: Given,f(x)=8x+79x+2

Q: х* — 5х — 5 f(x) х - 8

A: Consider the graph for the function:

Q: Show that the function f(x) = |x-3| is not differentiable at x = 3.

A:

Q: What conditions have to be checked to determine if a function is "well defined"?  How would I show…

A: Let the function beThen we need to check 3 conditions to prove that the function is Well definedThey…