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# Domain and Range

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Lana defines a function $f(x)$ which is given by the formula

$$f(x) = x^2,$$

but only on a domain, she has specified which consists of finitely many values $x$; she leaves the function undefined for all other $x$.

Given that the range of $f(x)$ is $\{0,1,2,3,4,5,6,7,8,9\}$, what is the maximum number of points that could be in its domain?

Feb 21, 2021

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$$\text{Domain} \quad \{0, 1, \sqrt{2}, \sqrt{3}, 2, \sqrt{5}. \sqrt{6}. \sqrt{7}, \sqrt{8}, 3\}$$

This is a total of 10 values.

Feb 21, 2021