Kindly explain step by step to solve this question √-x-XConsider the function, f(x)= { 3-x(x-3)²x < 00 3Decide whether f is continuous at 0 and 3; justify your answer byusing the definition of continuity.

Given: To Find: To decide whether is continuous at 0 and 3.

Answered: √=x Consider the function, f(x) = { 3-x…

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

Kindly explain step by step to solve this question

√-x
-X
Consider the function, f(x)= { 3-x
(x-3)²
x < 0
0<x<3
x > 3
Decide whether f is continuous at 0 and 3; justify your answer by
using the definition of continuity.

Expert Solution

Step 1: Define the problem.

Given:

$straight f open parentheses straight x close parentheses equals open curly brackets table row cell square root of negative straight x end root comma space straight x less than 0 end cell row cell 3 minus straight x comma space 0 less or equal than straight x less than 3 end cell row cell open parentheses straight x minus 3 close parentheses squared comma space straight x greater than 3 end cell end table close$

To Find:

To decide whether $f$ is continuous at 0 and 3.