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Liapis
Liapis
23.06.2019 • 
Mathematics

For each of the following, determine if the function is increasing, decreasing, even, odd, and/or invertible on its natural domain: $$f(x) = x^2 - 2x + 3$$ for each property, write increasing, decreasing, even, odd, invertible in that order (alphabetical). for example, if the function is increasing, odd, and invertible, submit "cov". if the function is none of the above, submit "none". terminology note: recall that for a function $f : \mathbb{r} \to \mathbb{r}$, the natural domain of $f$ is the largest domain $d$ you can take such that $f(x) \in \mathbb{r}$ for all $x \in d$. (here we mean "largest" in the sense of containment of sets. for sets $a$ and $b$, if $a \supset b$, then $a$ is "larger than" $b$.) to say it another way, the natural domain consists of all the real numbers $x$ you can feed into $f$ and get a real number $f(x)$ back as output. for example, the natural domain of $\sqrt{x}$ is $[0, \infty)$ because those are the real numbers $x$ such that $\sqrt{x}$ is real.

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