Combining functions - just another check

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The discussion focuses on the composition of the functions f(x) = 2/x and g(x) = x/(x+2). The composition fog is calculated as f(g(x)), leading to the expression 2*(x+2)/x. Participants emphasize the importance of using parentheses for clarity and the need to consider the domain of both functions to identify excluded values. The conversation highlights that without specifying the domain, the functions may not be considered valid. Understanding the domain is crucial for accurately defining the composition of functions.
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combining functions - just another check :)

f(x) = 2/x
g(x) = x/x+2

fog = f(g(x))
= f(x/x+2)
=2/x/x+2
=2 * x+2/x
=2x+2/x

[Edit (by ahrkron): no changes; took back my edit (I meant to reply)... the post is now in its original form]
 
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Better recheck the last two equations.
2*(x+2)/x is what you meant, is it not?
 
Be careful. Use parentheses, and you most probably need to think about the domain of both functions (what values of x are excluded on each case? what about the composition?).
 
oh ya, I forgot to distribute the 2

how would I find the domain ahrkron :redface:
 
For what values of x are f(x) and g(x) undefined? Those will be out of the domain.

cookiemonster
 
The domain should be given otherwise it isnt' a function. At some point teachers and basic textbook writers are going to learn this.
 
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