How does this composite function simplify to 2(2^x) ?

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Homework Help Overview

The discussion revolves around the simplification of a composite function involving exponential expressions, specifically focusing on the functions f(x) = 2x and g(x) = 2^x.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • Participants explore the definition of the composite function fg(x) and its simplification. There is a question regarding the equivalence of the expression 2(2^x) to 2^(x+1), prompting a discussion on the properties of exponents.

Discussion Status

Some participants have expressed confusion about the simplification process, while others have indicated they found clarity in the relationship between the expressions. The conversation reflects a mix of understanding and inquiry without reaching a definitive consensus.

Contextual Notes

One participant questioned the definition of 2^n, suggesting that definitions and properties of exponents are relevant to the discussion.

lioric
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f(x)=2xand g(x)=2^x
Find the composite function of fg(x)
fg(x)
=f(g(x))
=f(2^x)
=2(2^x)

I don’t understand how this in turn equals to 2^(x+1)

[Moderator's note: Moved from a technical forum and thus no template.]
 
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How is ##2^n## defined?
 
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Likes   Reactions: lioric
Never mind I got it
2^1 x 2^x = 2^(x+1)
 
Thank you anyway
 

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