How do you do this question
1 answer:
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that's what I got, you can confirm if it's correct or not... I'm not sure
have a nice dayʘ‿ʘ
To check if a piecewise defined function is continuous, you need to check how the pieces "glue" together when you step from one domain to the other.
So, the question is: what happens at x=3? If you reach x=3 from values slightly smaller than 3, you obey the rule f(x)=log(3x). So, as you approach 3, you get values closer and closer to
Similarly, if you reach x=3 from values slightly greater than 3, you obey the rule f(x)=(4-x)log(9). So, as you approach 3, you get values closer and closer to
So, the function is continuous at x=3, because both pieces approach log(9) as x approaches 3.