Question 629043
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The domain of a function is the set of all values of the independent variable for which the function exists.


The square root function exists mapped to the real numbers for all values of the independent variable for which the radicand is greater than or equal to zero.


Set up the inequality:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -25x^2\ +\ 60x\ -\ 36\ \geq\ 0]


I'll leave it as an exercise for you to demonstrate that there is exactly one value of *[tex \LARGE x] for which this inequality is true, and hence the domain consists of this single value.


On the other hand, if you map the function to the complex numbers, then the domain is all reals, thus:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \text{dom}\left(y\ :\ \mathbb{R}\,\rightarrow\,\mathbb{C},\ y(x)\ =\ \sqrt{60x\ -\ 25x^2\ -\ 36}\right)\ =\ \left{x\ \in\ \mathbb{R}\right}]


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
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