SOLUTION: 1. What is the relationship of input and output values for composite functions? 2. How you know if a radical expression is in simplest form? 3. How can you tell if radicals

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Question 685774: 1. What is the relationship of input and output values for composite functions?
2. How you know if a radical expression is in simplest form?
3. How can you tell if radicals are like radicals?
4. Is the inverse of a function always a function?

Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
1. What is the relationship of input and output values for composite functions?
If the composite is fog(x) the output of "g" is the input of "f".
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2. How you know if a radical expression is in simplest form?
If the problem is seeking the "nth" root, the expression will be
in simplest form when it contains no factors of n or greater power.
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3. How can you tell if radicals are like radicals?
Ans: When their simplified forms have the same radicand.
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4. Is the inverse of a function always a function?
Ans: No. Example--- The inverse of y = x^2 is not a function.
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Cheers,
Stan H.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

1.
In a composite function, the output of the inside function is the input of the outside+function.
That is, in f%28g%28x%29%29, the output of g%28x%29 is the input of f%28x%29.
2.
If the radicand contains no perfect square factors, the radical is in+simplest+form.
3.
Like radicals have the same radicand and the same index.
4.
The inverse of a function does+not have to be a function. In fact, the inverse of any even function is not a function when the domain is the real numbers.
For example, the inverse of y+=+x%5E2 is not a function unless the domain is limited to positive numbers.