Zad. 8.17.
a)
X = {0, 1, 8, 64}
[tex]f(0) = \sqrt[3]{0} =0 \\ f(1) = \sqrt[3]{1} =1 \\ f(8) = \sqrt[3]{8} =2 \\ f(64) = \sqrt[3]{64} =4[/tex]
Zbiór par uporządkowanych:
{(0, 0), (1, 1), (8, 2), (64, 4)}
b)
X = {- 4, - 2, - 1, 1, 2, 3, 4}
[tex]f(-4) =\frac{1}{-4} +1=-\frac{1}{4} +1=\frac{3}{4} \\\\ f(-2) =\frac{1}{-2} +1=-\frac{1}{2} +1=\frac{1}{2} \\\\ f(-1) =\frac{1}{-1} +1=-1+1=0 \\\\ f(1) = \frac{1}{1} +1=1+1=2 \\\\ f(2) =\frac{1}{2} +1=1\frac{1}{2} \\\\ f(3) =\frac{1}{3} +1=1\frac{1}{3} \\\\ f(4) =\frac{1}{4} +1=1\frac{1}{4}[/tex]
Zbiór par uporządkowanych:
[tex]\{(-4, \ \frac{3}{4}), \ (-2, \ \frac{1}{2}), \ (-1, 0), (1, \ 2), \ (2, \ 1\frac{1}{2}), \ (3, \ 1\frac{1}{3}), \ (4, \ 1\frac{1}{4}) \}[/tex]
c)
[tex]X = \{-3, \ -2\frac{1}{2}, \ -1, \ 1\frac{1}{3}, \ 2, \ 3\frac{2}{5} \} \\\\ f(-3) = - 3 \cdot (-2) - 4 = 6-4 = 2 \\\\ f(-2\frac{1}{2}) =-2\frac{1}{2} \cdot (-2) - 4 =-\frac{5}{\not{2}_1}\cdot (-\not{2}^1) - 4 =5 - 4=1 \\\\ f(-1) = - 1 \cdot (-2) - 4 = 2-4 = -2 \\\\ f(1\frac{1}{3}) =1\frac{1}{3}\cdot (-2) - 4 =\frac{4}{3}\cdot (-2) - 4 =-\frac{8}{3} - 4=-2\frac{2}{3} - 4=-6\frac{2}{3} \\\\ f(2) = 2 \cdot (-2) - 4 = -4-4 = -8[/tex]
[tex]f(3\frac{2}{5}) =3\frac{2}{5} \cdot (-2) - 4 =\frac{17}{5} \cdot (-2) - 4 =-\frac{34}{5} - 4=-6\frac{4}{5} - 4=-10\frac{4}{5}[/tex]
Zbiór par uporządkowanych:
[tex]\{(-3, \ 2), \ (-2\frac{1}{2}, \ 1), \ (-1, \ -2), \ (1\frac{1}{3}, \ -6\frac{2}{3}), \ (2, \ -8), \ (3\frac{2}{5}, \ -10\frac{4}{5})\}[/tex]
d)
X = {- 3, - 2, - 1, 0, 1, 4, 5, 9}
f(- 3) = - (- 3)² = - 9
f(- 2) = - (- 2)² = - 4
f(- 1) = - (- 1)² = - 1
f(0) = - 0² = 0
f(1) = - 1² = - 1
f(4) = - 4² = - 16
f(5) = - 5² = - 25
f(9) = - 9² = - 81
Zbiór par uporządkowanych:
{(- 3, - 9), (- 2, - 4), (- 1, - 1), (0, 0), (1, - 1), (4, - 16), (5, - 25), (9, - 81)}