Combining functions - just another check

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In summary, combining functions involves using one function's output as another function's input. The composition of f(x) and g(x) is written as fog and is found by plugging g(x) into f(x). In this case, fog = 2x+2/x. However, it is important to note that the domain of both functions must be considered, as values of x that make either f(x) or g(x) undefined will also make fog undefined.
  • #1
Agent_J
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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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  • #2
Better recheck the last two equations.
2*(x+2)/x is what you meant, is it not?
 
  • #3
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?).
 
  • #4
oh ya, I forgot to distribute the 2

how would I find the domain ahrkron :redface:
 
  • #5
For what values of x are f(x) and g(x) undefined? Those will be out of the domain.

cookiemonster
 
  • #6
The domain should be given otherwise it isnt' a function. At some point teachers and basic textbook writers are going to learn this.
 

FAQ: Combining functions - just another check

Can you explain what it means to combine functions?

Combining functions is the process of taking two or more functions and creating a new function that performs the operations of both functions. This allows for more efficient and concise problem-solving in mathematics and science.

What are the steps to combine two functions?

The steps to combine two functions are as follows: 1) Rewrite the functions in terms of a common variable. 2) Simplify the functions by combining like terms. 3) Substitute the simplified functions into a new function. This new function is the combined function.

Can any two functions be combined?

Yes, any two functions can be combined as long as they share a common variable. However, the resulting combined function may not always be simplified or have a closed form expression.

How can combining functions be useful in scientific research?

Combining functions can be useful in scientific research as it allows for more efficient calculation and analysis of data. It also allows for the creation of new functions that can model and predict complex phenomena.

Are there any limitations to combining functions?

One limitation of combining functions is that the resulting combined function may not always have a closed form expression. This can make it difficult to analyze or graph the function. Additionally, combining functions may not always accurately represent real-world situations due to simplifications made during the process.

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