College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter2: Functions And Graphs
Section2.CT: Chapter Test
Problem 4CT: Find f(1) and f(2). f(x)=x+7
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Question
Find the constant a such that this function g(x) is continuous on the entire number line.
Expert Solution
Step 1
Given,
Step 2
g(x) is continuous for all x < 0, as both sinx and x are continuous.
g(x) is continuous for all x > 0, as a - 3x is a linear equation which represents a straight line.
Now we check the continuity of g(x) at x = 0:
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