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1 برای هریک از توابع زیر، دامنه و بُرد را مشخص کنید و در صورت امکان ضابطهٔ هر تابع را بنویسید.
الف
\(\begin{array}{l}A = \left\{ { - 1\,,\,1\,,\,2\,,\,3\,,\,4} \right\}\\\\{R_f} = \left\{ { - 1\,,\,0\,,\,1\,,\,3} \right\}\end{array}\)
ب
\(\begin{array}{l}A = \left\{ {0\,,\,1\,,\,2\,,\,3\,,\,4} \right\}\\\\{R_f} = \left\{ 2 \right\}\\\\ \Rightarrow f(x) = 2\end{array}\)
پ
\(\begin{array}{l}A = \left\{ { - 2\,,\, - 1\,,\,0\,,\,1\,,\,2\,,\,3\,,\,4} \right\}\\\\{R_f} = \left\{ {0\,,\,1\,,\,2\,,\,3} \right\}\\\\ \Rightarrow f(x) = x + 2\end{array}\)
ت
\(\begin{array}{l}A = \left[ { - 1\,,\,4} \right]\\\\{R_f} = \left[ { - 1\,,\,4} \right]\\\\ \Rightarrow f(x) = x\end{array}\)
2 دامنه و برد هریک از تابع های زیر را مشخص کنید.
الف
\(\begin{array}{l}f:A \to B\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{R_f} = \left\{ {2\,,\,3\,,\,4\,,\,5\,,\, \cdots } \right\}\\\\f(x) = x + 4\,\,\,\,\,\,\,A = \left\{ {2\,,\, \cdots \,,\, \cdots \,,\, \cdots \,,\, \cdots } \right\}\end{array}\)
ب
\(f = \left\{ {(1\,,\, - 1)\,,\,(2\,,\, - 2)\,,\,(3\,,\, - 3)\,,\,(4\,,\, - 4)\,,\,(\sqrt 2 \,,\, - \sqrt 2 )} \right\}\)
پ
ت
ث
\(f = \left\{ {(1\,,\,1)\,,\,(2\,,\,2)\,,\,(3\,,\,3)\,,\,(\frac{1}{2}\,,\,\frac{1}{2})\,,\,(\sqrt 2 \,,\,\sqrt 2 )\,,\,(0\,,\,0)} \right\}\)
الف
\(\begin{array}{l}f:A \to B\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{R_f} = \left\{ {2\,,\,3\,,\,4\,,\,5\,,\,6} \right\}\\\\f(x) = x + 4\,\,\,\,\,\,\,A = \left\{ {2\,,\, - 2\,,\, - 1\,,\,0\,,\,1} \right\}\end{array}\)
ب
\(\begin{array}{l}f = \left\{ {(1\,,\, - 1)\,,\,(2\,,\, - 2)\,,\,(3\,,\, - 3)\,,\,(4\,,\, - 4)\,,\,(\sqrt 2 \,,\, - \sqrt 2 )} \right\}\\\\A = \left\{ {1\,,\,2\,,\,3\,,\,4\,,\,\sqrt 2 } \right\}\\\\{R_f} = \left\{ { - 1\,,\, - 2\,,\, - 3\,,\, - 4\,,\, - \sqrt 2 } \right\}\end{array}\)
پ
\(\begin{array}{l}A = \left\{ {7\,,\,5\,,\,4\,,\, - 1\,,\,0} \right\}\\\\{R_f} = \left\{ {4\,,\,2\,,\,1\,,\, - 4\,,\, - 3} \right\}\end{array}\)
ت
\(\begin{array}{l}A = \left\{ {1\,,\,2\,,\,3\,,\,4\,,\,5} \right\}\\\\{R_f} = \left\{ 1 \right\}\end{array}\)
ث
\(\begin{array}{l}A = \left\{ {1\,,\,2\,,\,3\,,\,\frac{1}{2}\,,\,\sqrt 2 ,\,0} \right\}\\\\{R_f} = \left\{ {1\,,\,2\,,\,3\,,\,\frac{1}{2}\,,\,\sqrt 2 ,\,0} \right\}\end{array}\)
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