Question

find the values of the constants a and/or b needed to make the following functions continuous for all real numbers x

piecewise f(x) = ax - 12/x - 3, if x not equal to 3, b, if x = 3

Expert Solution

Want to see the full answer?

Check out a sample Q&A here
Blurred answer
Students who’ve seen this question also like:
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN: 9781337278461
Author: Ron Larson
Publisher: Cengage Learning
Not helpful? See similar books
Trigonometry (MindTap Course List)
marketing sidebar icon
Want to see this answer and more?
Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*
*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.

Related Calculus Q&A

Find answers to questions asked by students like you.

Q: Determine where the following function is continuous. X- 1 M(x) = 9x2. - 16 The function is…

A: Click to see the answer

Q: Let f be the function (8x-1 for x х Find the values of a and b that make the function continuous.

A: Click to see the answer

Q: Given the function f (x) = 3x25 – 6x24. Determine the intervals for which the function - is…

A: Click to see the answer

Q: Find the constant a such that the function is continuous on the entire real line. (9x², Flx) = {9x?,…

A: Given function is : fx=9x2    ,      x≥1ax-6   ,    x<1 Here given that function is continuous…

Q: Find a value for the constant k, if possible, that will make the function continuous. kox+1 for x 3

A: K = 1/3

Q: For the function given by f(x) = 2x2 - 8 divided by x2 -1 , find the intervals where the function is…

A: Click to see the answer

Q: For what value of x is the function f(x)=4/ x2-x-12 not continuous

A: Topic-continuity

Q: Find the value of k that makes function continuous at x = 4 3x + 6 x > 4 f(æ) = 6x – k x <4

A: Click to see the answer

Q: IS The function f(x)=\x3 Find The value of K, to continue The Function Con tinuous in intervaln X-2…

A: Answer

Q: Determine whether the function f(x)=5+3x if x <4…

A: Click to see the answer

Q: Determine if the function f(x) is continuous and/or differentiable at x = 1? x +5 for - 1sxS1 f(x) =…

A: The given function is f(x)=x+5    for -1≤x≤16x       for  1&gt;x≤4 The function is said to be…

Q: Find the values of x for which the function is continuous. (Enter your answer using interval…

A: The function is given as fx=4-x      if x&lt;3 2x-5    if x≥3 find values of x for which the…

Q: 2. Given that f(x) = Vx+1 and g(x) =x² -9, find |(x) and give its domain in interval notation.

A: Click to see the answer

Q: For what value of the constant c is the function f continuous on (-∞, 0)? cx2 + 8x x3 - cx if x < 5…

A: Click to see the answer

Q: Find (without using a calculator) the absolute extreme values of the function on the given interval.…

A: NOTE: Refresh your page if you can't see any equations. . to find the extreme point, take…

Q: Find the constant a such that the function is continuous on the entire real line. (8x?, lax – 6, x2…

A: Given function f(x) = 8x2-x≥1ax-6, x&lt;4we find constant 'a' such that the function is continuous…

Q: Determine where the following function is continuous. x-4 M(x) = 9x2 - 25 The function is continuous…

A: Click to see the answer

Q: find continuity of the following function on its domain: f(x) = Root of x^2-4

A: The given function is  f(x)=x2-4

Q: Find a value of the constant k, if possible, that will make the function continuous everywhere. (kx…

A: Click to see the answer

Q: Use the definitions of increasing and decreasing functions to prove that       f(x) = x3 is…

A: Click to see the answer

Q: Suppose f(x) is a twice-differentiable function which is positive and decreasing for all real…

A: Consider the given conditions for f(x) and assume the graph for function f(x) for the given…

Q: The piecwise function g(x) is defined by x + 2 when x 1. What type of discontinuites are present in…

A: Click to see the answer

Q: Determine if the function is continuous or discontinuous at x = 2. x2 - 1, if x 22 h(x) = 2x-1, if…

A: We have to find

Q: he first principle to determine f'(x) of the following functions: f(x)=x2 f(x)=x2-

A: f(x) = x2 ddx(f) = f'(x) = 2x

Q: Find the value of K that makes 4-x2 f(x) = {2-x if x # 2 2K if x = 2 continuous at x = 2 ?

A: Find the value of k

Q: Find the numbers at which f is discontinuous. Show your work like in Example 34 from x2, x4

A: As per our company's guideline, we need to answer only one question at a time. Please repost the…

Q: Find the open intervals where the function f(x)=-2/x+1 is concave up and concave down. State any…

A: According to the given information, it is required to calculate the interval where the function is…

Q: Suppose we know that f(x) is continuous and differentiable on the interval [-8, 0], that f(-8) = -9,…

A: Given data: The value of function is, f(-8)=-9 The value of differentiating function  f(x)≤2

Q: If the function f (x) is continuous for all real numbers and if f (x) x²-4 when x + -2, then x+2 f…

A: f(-2) = -4

Q: Determine the whether the function is continuous at x=-2. Justify your answer 2x+7 if xS-2 using the…

A: Click to see the answer

Q: Find the constant a such that the function is continuous on the entire real line. 7sin x if x <0…

A: For a function to be continuous at x = a, it must satisfy the following condition:

Q: Is the function f(x) : 1 continuous or discontinuous on [2,+∞)? Vx - 2 Is the function f(x) : 1…

A: Click to see the answer

Q: On the graph of f(x) = cotx and the interval [ − 2π, 0π ), for what value(s) of x does f(x) = 1

A: Given, fx = cotx   and the interval [-2π, 0) We have to find the values of x for which fx = 1

Q: 2, if x -1 Find the value for a and b such that f (x) = {ax + b, if – 1 3 for all real numbers.

A: NOTE: Refresh your page if you can't see any equations. . the function is continuous at x=-1 so we…

Q: Find the intervals in which the function f(x) = x4 – 8x3 – 5 is concave up/concave down. Also find…

A: From the given problem:   fx=y=x4-8x3-5   As we know that:   a). For concave upward f''x or…

Q: Determine where the following function is continuous. X-1 M(x) = 4x - 81 The function is continuous…

A: Click to see the answer

Q: 3) Find the value of k that makes function continuous at x = 4 Зх + 8 x > 4 f(x) = 4x – k x < 4 — k

A: A function is a relation from a set of inputs to a set of possible outputs where each input is…

Q: Find the interval on which f(x) = x² + 4x – 1 is increasing and the interval upon which it is…

A: Click to see the answer

Q: The domain of f' is 1 (Type your answer in interval notation.)

A: Click to see the answer

Q: On what domain is the function f(x) = 3x + 5x + 6 continuous?

A: The given function is, fx=3x2+5x+6

Q: x²-1 for x +1 and f(x)=2 when x=1, show that the function X-1 If f(x) =- is continous at x-1?

A: A function f is continuous at a point x=a if limx→af(x)=f(a), that is, the limit of a function at a…

Knowledge Booster
Calculus
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Recommended textbooks for you
  • Trigonometry (MindTap Course List)
    Trigonometry
    ISBN:9781337278461
    Author:Ron Larson
    Publisher:Cengage Learning
    College Algebra
    Algebra
    ISBN:9781938168383
    Author:Jay Abramson
    Publisher:OpenStax
    College Algebra (MindTap Course List)
    Algebra
    ISBN:9781305652231
    Author:R. David Gustafson, Jeff Hughes
    Publisher:Cengage Learning
  • Algebra & Trigonometry with Analytic Geometry
    Algebra
    ISBN:9781133382119
    Author:Swokowski
    Publisher:Cengage
    Big Ideas Math A Bridge To Success Algebra 1: Stu...
    Algebra
    ISBN:9781680331141
    Author:HOUGHTON MIFFLIN HARCOURT
    Publisher:Houghton Mifflin Harcourt
    Algebra: Structure And Method, Book 1
    Algebra
    ISBN:9780395977224
    Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
    Publisher:McDougal Littell
  • Trigonometry (MindTap Course List)
    Trigonometry
    ISBN:9781337278461
    Author:Ron Larson
    Publisher:Cengage Learning
    College Algebra
    Algebra
    ISBN:9781938168383
    Author:Jay Abramson
    Publisher:OpenStax
    College Algebra (MindTap Course List)
    Algebra
    ISBN:9781305652231
    Author:R. David Gustafson, Jeff Hughes
    Publisher:Cengage Learning
    Algebra & Trigonometry with Analytic Geometry
    Algebra
    ISBN:9781133382119
    Author:Swokowski
    Publisher:Cengage
    Big Ideas Math A Bridge To Success Algebra 1: Stu...
    Algebra
    ISBN:9781680331141
    Author:HOUGHTON MIFFLIN HARCOURT
    Publisher:Houghton Mifflin Harcourt
    Algebra: Structure And Method, Book 1
    Algebra
    ISBN:9780395977224
    Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
    Publisher:McDougal Littell