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Apuntes

• Subtopic: Function and Domain Analysis 1. EBALUAKETA 1. gaia: Funtzioa I 1. FUNTZIOA ETA MUGEN AZTERKETA In this section, we will analyze functions and their domains. The domain of a function is the set of values that the variable $x$ can take. The range is the set of values that the variable $y$ can take. 2. Definizio - eremua Adibideak: Aurkitu definizio-eremua funtzio hauetan (Find the domain of these functions): a) $y = x - 5$ - $x - 5 = 0 \Rightarrow x = 5$ - $Dom \, f = \mathbb{R} - \{5\}$ b) $y = \frac{2x}{x^3}$ - $x \neq 0$ - $Dom \, f = \mathbb{R} - \{0\}$ c) $y = \frac{1}{x - 3}$ - $x - 3 = 0 \Rightarrow x = 3$ - $Dom \, f = \mathbb{R} - \{3\}$ d) $y = x^2 - 2x + 4$ - $x^2 - 2x + 4 = 0$ - $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \frac{-(-2) \pm \sqrt{(-2)^2 - 4(1)(4)}}{2(1)}$ - $x = \frac{2 \pm \sqrt{4 - 16}}{2}$ e) $y = \frac{x}{x^2 - 16}$ - $x^2 = 16 \Rightarrow x = \pm \sqrt{16} \Rightarrow x = \pm 4$ - $Dom \, f = \mathbb{R} - \{-4, 4\}$ f) $y = \frac{1}{x - 5}$ - $x - 5 = 0 \Rightarrow x = 5$ - $Dom \, f = \mathbb{R} - \{5\}$ g) $y = \sqrt{x^2 - 3x}$ - $x^2 - 3x = 0 \Rightarrow x(x - 3) = 0$ - $x = 0...