شاه کلید نکات
شاه کلید سوال
اگر \(f\left( x \right) = \frac{2}{{x - 1}}\) و\(g\left( x \right) = \frac{3}{x}\) ، دامنه و ضابطهٔ توابع fog و fof را به دست آورید.
\(\begin{array}{l}fog(x) = \frac{2}{{g(x) - 1}} = \frac{2}{{\frac{3}{x} - 1}} = \frac{{2x}}{{3 - x}}\\\left\{ \begin{array}{l}{D_f} = \mathbb{R} - \left\{ 1 \right\}\\{D_g} = \mathbb{R} - \left\{ 0 \right\}\end{array} \right.\quad \Rightarrow \quad {D_{fog}} = \left\{ {x \in {D_g}|g(x) \in {D_f}} \right\} = \\\\\left\{ {x \ne 0|\frac{3}{x} \ne 1} \right\} = \left\{ {x \ne 0|x \ne 3} \right\} = \mathbb{R} - \left\{ {0\;,\;3} \right\}\\\\fof(x) = \frac{2}{{f(x) - 1}} = \frac{2}{{\frac{2}{{x - 1}} - 1}} = \frac{{2x - 2}}{{3 - x}}\\ \Rightarrow \quad {D_{fof}} = \left\{ {x \in {D_f}|f(x) \in {D_f}} \right\} = \\\\\left\{ {x \ne 1|\frac{2}{{x - 1}} \ne 1} \right\} = \left\{ {x \ne 1|x \ne 3} \right\} = \mathbb{R} - \left\{ {0\;,\;3} \right\}\end{array}\)
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