Question

(a) Find the constants a and b such that the function is continuous on the entire real number line. f(x) = { 1 + x, 0 ? x ? 1 x - a, 1 < x ? 3 (x - 4)² + b, 3 < x ? 5 (b) Find all x-values at which f is not continuous. Which of the discontinuities are removable? f(x) = (x² - 2x - 3) / (2x² - 5x - 3)

          (a) Find the constants a and b such that the function is continuous on the entire real number line.

f(x) = {
1 + x, 0 ? x ? 1
x - a, 1 < x ? 3
(x - 4)² + b, 3 < x ? 5

(b) Find all x-values at which f is not continuous. Which of the discontinuities are removable?

f(x) = (x² - 2x - 3) / (2x² - 5x - 3)

(a) Find the constants a and b such that the function is continuous on the entire real number line.

f(x) =
1 + x, 0 ? x ? 1
x - a, 1 < x ? 3
(x - 4)² + b, 3 < x ? 5

(b) Find all x-values at which f is not continuous. Which of the discontinuities are removable?

f(x) = (x² - 2x - 3) / (2x² - 5x - 3)

Added by Nathan M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Andrew Noble

09/09/2022

Step 1

At x = 1: 1 + 1 = 1 - a 2 = 1 - a a = -1 At x = 3: 3 + 1 = (3 - 4)^2 + b 4 = 1 + b b = 3 Therefore, the constants a = -1 and b = 3 make the function continuous on the entire real number line. ** Show more…

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(a) Find the constants a and b such that the function is continuous on the entire real number line. f(x) = 1+x, 0<=x<=1 x-a, 1<x<=3 (x-4)^2+b, 3<x<=5 (b) Find all x-values at which f is not continuous. Which of the discontinuities are removable? f(x) = (x^2 - 2x - 3) / (2x^2 - 5x - 3)