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Bestimme die Summe, die Differenz, das Produkt und den Quotienten von $$$f{\left(x \right)} = x - 2$$$ und $$$g{\left(x \right)} = \frac{1}{x}$$$
Verwandter Rechner: Rechner für Funktionskomposition
Ihre Eingabe
Bestimme die Summe, die Differenz, das Produkt und den Quotienten von $$$f{\left(x \right)} = x - 2$$$ und $$$g{\left(x \right)} = \frac{1}{x}$$$.
Lösung
$$$\left(f + g\right)\left(x\right) = {\color{red}\left(x - 2\right)} + {\color{red}\left(\frac{1}{x}\right)} = \frac{\left(x - 1\right)^{2}}{x}$$$
$$$\left(f - g\right)\left(x\right) = {\color{red}\left(x - 2\right)} - {\color{red}\left(\frac{1}{x}\right)} = x - 2 - \frac{1}{x}$$$
$$$\left(f\cdot g\right)\left(x\right) = {\color{red}\left(x - 2\right)}\cdot {\color{red}\left(\frac{1}{x}\right)} = \frac{x - 2}{x}$$$
$$$\left(\frac{f}{g}\right)\left(x\right) = \frac{{\color{red}\left(x - 2\right)}}{{\color{red}\left(\frac{1}{x}\right)}} = x \left(x - 2\right)$$$
Antwort
$$$\left(f + g\right)\left(x\right) = \frac{\left(x - 1\right)^{2}}{x}$$$A
$$$\left(f - g\right)\left(x\right) = x - 2 - \frac{1}{x}$$$A
$$$\left(f\cdot g\right)\left(x\right) = \frac{x - 2}{x}$$$A
$$$\left(\frac{f}{g}\right)\left(x\right) = x \left(x - 2\right)$$$A