Find the value of the constant c so the function f is continuous on (-∞, ∞) wheref(y) =-[cy +9if y ≤ 8[c(y)² – 9 if y>8

To find the value of the constant so that the function is continuous on where

Answered: Find the value of the constant c so the…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

Find the value of the constant c so the function f is continuous on (-∞, ∞) where
f(y) =
-
[cy +9
if y ≤ 8
[c(y)² – 9 if y>8

Expert Solution

Step 1: Define the problem.

To find the value of the constant $straight c$ so that the function $straight f$

is continuous on $open parentheses negative infinity comma space infinity close parentheses$ where

$straight f open parentheses straight y close parentheses equals open curly brackets table row cell cy plus 9 space if space straight y less or equal than 8 end cell row cell straight c open parentheses straight y close parentheses squared minus 9 space if space straight y greater than 8 end cell end table close$