Comparing the domains of composite functions

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The discussion revolves around verifying the correctness of a solution regarding the domains of composite functions. The original poster has shared their work and is seeking confirmation on their answer. Participants are encouraged to review the provided details to ensure accuracy. The use of LaTeX for clarity in mathematical expressions is acknowledged as beneficial. The thread emphasizes the importance of understanding composite function domains in mathematics.
srfriggen
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Homework Statement
The problem and solution are posted in an attachment.
Relevant Equations
h(x) = f(g(x)) and more are in attachment.
Hello,

I have attached my question and the work. I believe the answer is correct. Looking for verification.

Thank you!
 

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Must be easier with Latex, but correct.
 
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