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

Thread starter lioric
Start date Sep 12, 2019
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Composite Composite function Function Simplify

In summary, the composite function is determined by plugging the inner function into the outer function. Simplifying a composite function allows for easier analysis and understanding. The steps to simplify a composite function to 2(2^x) are: first, plug the inner function into the outer function, then distribute the 2, and finally combine like terms. Depending on the given functions, the composite function may simplify to a different form, but in this case, it simplifies to 2(2^x). You can check if your simplified composite function is correct by plugging in values for x and comparing the output to the original function. If the outputs match, then the simplified composite function is correct.

Sep 12, 2019

lioric

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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Sep 12, 2019

fresh_42

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How is ##2^n## defined?

Sep 12, 2019

lioric

Never mind I got it
2^1 x 2^x = 2^(x+1)

Sep 12, 2019

lioric

Thank you anyway

1. How do I simplify a composite function?

To simplify a composite function, you need to first identify the inner function and the outer function. Then, you can use the chain rule to differentiate the function and simplify it accordingly.

2. What is the purpose of simplifying a composite function?

The purpose of simplifying a composite function is to make it easier to understand and work with. It also allows for easier calculations and analysis of the function.

3. Can a composite function always be simplified to 2(2^x)?

No, a composite function cannot always be simplified to 2(2^x). It depends on the specific function and its components. Some composite functions may have different simplifications or may not have a simplified form at all.

4. Are there any specific rules or formulas for simplifying composite functions to 2(2^x)?

There are no specific rules or formulas for simplifying composite functions to 2(2^x). It depends on the individual components of the function and the specific steps taken to simplify it.

5. Is it necessary to simplify a composite function to 2(2^x) or can it be left in its original form?

It is not necessary to simplify a composite function to 2(2^x). It depends on the purpose of the function and the preference of the person working with it. In some cases, leaving the composite function in its original form may be more useful or relevant.