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

AI Thread Summary
The composite function of f(x) = 2x and g(x) = 2^x simplifies to fg(x) = f(g(x)) = 2(2^x). There was confusion regarding how this expression relates to 2^(x+1). It was clarified that 2(2^x) can be rewritten as 2^1 * 2^x, which equals 2^(x+1). The discussion highlights the importance of understanding exponent rules in simplifying composite functions. Overall, the key takeaway is the relationship between the expressions through exponent properties.
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 lioric
Never mind I got it
2^1 x 2^x = 2^(x+1)
 
Thank you anyway
 
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