### Algebraic Functions

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Then divide both sides by Finally, re-write the expression that is equal to , replacing the with an :. The inverse function of is:. You can check your answer by seeing if does reverse. For example, and. Function notation — Higher A function links an input value to an output value. Example and Find and Composite functions Composite functions are made when the output from one function is used as the input of another function.

Example and Find , and means work out , then work out for this value. Zbl Dvornicich - U.

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Zannier , Fields containing values of algebraic functions. Preprint Univ. Pisa Novembre MR Number Theory 6 , Fried - M. Jarden , Field Arithmetic.

Springer-Verlag Hooley , Applications of sieve methods to the theory of numbers. Cambridge Tracts in Mathematics , Cambridge Univ. Press, Lang , Algebraic Number Theory.

Addison Wesley Lang , Fundamentals of Diophantine Geometry. That's going to be undefined.

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And if what you have another radical is negative, the principal root isn't defined for native number, at least the classic principal root is a defined for a negative number. So if 6 minus the absolute value of x is zero or negative, this thing is not going to be defined.

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Or another way to think about it is it's going to be defined -- so g is is defined -- is defined if -- g is defined if 6 minus, maybe I can write if and only if. Sometimes people write if and only if with two f's right there, iff.

If it's zero, we're going take the square root of 0 is 0. Then you divide by 0. That's undefined. And if it's less than zero, then you're taking, you're trying to find the principal root of a negative number, that's not defined. So let's see, it's g is defined if and only if this is true. And let's see.

## [PDF] Algebraic Functions, Computer Programming, and the Challenge of Transfer - Semantic Scholar

We could add the absolute value of x to both sides. We could add the absolute value of x to both sides, then that would give us 6 is greater than the absolute value of x, or that the absolute value of x is less than 6. Or we could say that, you know, let me write that way.

The absolute value of x is less than 6. Another way of saying that is x would have to be less than 6 and greater than negative 6. These two things -- these two things are equivalent. If the magnitude of x is less than 6 then x is greater than negative 6 and less than positive 6. So if we wanted to write the domain in kinda fancy domain-set notation, we could write the domain of g is going to be x, all the x's that are a member of real numbers such that negative 6 is less than x, which is less than 6, and we're done. Let's do another one. And this was gonna get even a little bit a little bit hairier, just for, just for kicks.

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So let's say that I have -- let's say that I have -- h of x is equal to -- and I have a kind of composite definition here. So let's say it's x plus 10 over x plus 10 times x minus 9 times x minus 5 times x minus 5 and it's this if it -- h of x is this if x does not equal 5 and it's equal to -- it's equal to pi if x is equal if x is equal to 5. So once again, pause this video. Think about what is the domain of h, or another way to think about is what made h not defined? So let's think about it. So what would make h not defined? So if some -- if x is anything other than 5, we go this clause.

If it's 5, we go this clause. So in this clause up here, what would make this thing undefined?