Solving Composite Functions with Simple Examples

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The discussion centers on solving the composite function gf(1) where g(x) = x² and f(x) = 2x + 1. The user is confused about whether to substitute 1 into x first or expand the function before substitution. They explore two approaches: substituting directly into (2x + 1)² and expanding it to 4x² + 4x + 1 before substituting. The user expresses frustration over the discrepancy between their calculations and the book's answer of 1. Ultimately, clarity on the correct method for evaluating composite functions is sought.
Peter G.
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I was doing some exercises on composite functions and I got all of the questions right but I can't figure this one out! :cry:

gf (1) where g = x2 and f = 2x + 1

So, (2x + 1)2

Now I don't know if I sub 1 into x already or if I expand, but, anyhow, I don't know how the book got 1 as an answer!

Thanks,
Peter G.
 
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Maybe the book answer was wrong!:redface:
 
Yes, I think so! :-p

So, what is right: (2x + 1)2 then, therefore, 2 + 1 = 3, and 32 = 9

or: (2x + 1)2 = (2x + 1) (2x + 1) = 4x2 + 4x + 1, then, sub 1?

Thanks,
Peter G.
 
:smile:
Whatever !
 
Ok, thanks for the help! :smile:
 

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