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ความสัมพันธ์และฟังก์ชัน

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áºº½ƒ¡ËÑ́ 1 1. ¨§à¢ÕÂ¹â´àÁ¹áÅÐàÃ¹ �̈¢Í§¤ÇÒÁÊÑÁ¾Ñ¹¸�áººá¨¡á¨§ÊÁÒªÔ¡

1) r={(3,5),(7,9),(11,13),(15,17)}

2) r={(x,y)∈I+×I+|x+y=12}

3) r={(x,y)∈A×A|x≥y} àÁ×èÍ A={3,4,5,6,7}

4) r={(x,y)∈B×B|y=x2} àÁ×èÍ B=�x∈I|-8≤x≤10�


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2. ¨§à¢ÕÂ¹â´àÁ¹áÅÐàÃ¹ �̈¢Í§¤ÇÒÁÊÑÁ¾Ñ¹¸� 1) r={(x,y)|y=x2+1}

2) r=�(x,y)�y=x2-5�

3) r={(x,y)|y=|x|}


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4) r={(x,y)|y=|x|+3}

5) r=�(x,y)�y=�x-1��

6) r=�(x,y)�y=|x+3|-2�

7) r= �(x,y)�y=�x-3�


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8) r=�(x,y)�y=-√5x+8�

9) r= �(x,y)�y=�x2-16�

10) r= �(x,y)�y= 3x-2

x-3�

11) r= �(x,y)�y= 4x+1

5-2x�


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áºº½ƒ¡ËÑ́ ·Õè 2 ¨§à¢ÕÂ¹¡ÃÒ¿áÊ´§¤ÇÒÁÊÑÁ¾Ñ¹¸� ¾ÃŒÍÁ·Ñé§ËÒâ´àÁ¹ �̈áÅÐàÃ¹ �̈

1) r=�(x,y)�y≤3x-2�

2) r=�(x,y)�y<3x2-12�

3) r=�(x,y)�y≥x2-4 áÅÐ 3x-y+6≥0�


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4) r=�(x,y)�-3<y≤1 áÅÐ x2+y2<16�

5) r={(x, y)∈RxR | x2+y2+4x+6y-3=0


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áºº½ƒ¡ËÑ́ 3

¨§ËÒ r-1, Dr-1, R

r-1 àÁ×èÍ¡íÒË¹´

1) r=�(x, y)�y=√x+5�

2) r= �(x, y)�y=�25-x2�


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3) r={(1, a),(2,b),(3,c)}

4) r=�(x, y)�y=5x-3�

5) r={(x, y)|y=x2+9}


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áºº½ƒ¡ËÑ́ 4 1. ¤ÇÒÁÊÑÁ¾Ñ¹¸�µ‹Íä»¹Õéà»š¹¿˜§¡�ªÑ¹ËÃ×ÍäÁ‹ ¶ŒÒà»š¹¨§ËÒ Df, Rf

1.1 r={(2,p),(3,q),(4,r)}

1.2 r={(2,a),(3,a),(4,a)}

1.3 r={(1,a),(2,b),(3,c),(1,d)}


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1.4 r={(x,y)|y=3x+1}

1.5 r= �(x,y)�y=�9-x2�

1.6 r= �(x,y)�x=�16-y2�

1.7 r={(x,y)|y=|x+3|}


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2. ¨§ËÒâ´àÁ¹áÅÐàÃ¹ �̈¨Ò¡¿§̃¡�ªÑ¹¡íÒÅÑ§ÊÍ§

2.1 f(x)=x2+5

2.2 f(x)=-x2-3

2.3 f(x)=-3�x-1�2


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2.4 f(x)=(x+4)2

2.5 f(x)=-2�x-1�2+5

2.6 f(x)=5(x+3)2-2

2.7 f(x)=x2-2x-15


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3. ¨§ËÒ f-1(x), Df-1, R

f-1

3.1 f(x)=3x-2

3.2 f(x)= 2x-5

x+2

3.3 f(x)=�x-3


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3.4 f(x)=3√x+4

3.5 f(x)= �7x+2 ,x≥05x+2 ,x≤0


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4. ¡íÒË¹´ f(2x+1)=4x-5 ¨§ËÒ f-1�3x-1�

5. ¡íÒË¹´ f(3x+2)=5x-1 ¨§ËÒ f-1(4x+7)


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6. ¡íÒË¹´ f-1�4x-3�=5x+2 ¨§ËÒ f�2x-9�

7. ¡íÒË¹´ f�2x-1�=x2-3x+4 ¨§ËÒ f(x)


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áºº½ƒ¡ËÑ́ 5

1. ¡íÒË¹´ f={�-2, 5�,�-1, 7�,(0, 9),(1, 11),(2, 13),(3, 15)} g={�-1, 6�,(0, 8),(2, 10),(3, 12),(5, -5)}

¨§ËÒ f+g, f-g, f∙g , fg, g-f


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2. ¡íÒË¹´

f(x)=2x-3, g(x)=3x-5 ¨§ËÒ (f+g)(x), �f-g�(x), (f∙g)(x), �f

g� (x)

¾ÃŒÍÁ·Ñé§ËÒâ´àÁ¹


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3. ¡íÒË¹´ f(x)= 1

3x2-x-2, g(x)= x

x-1 ¨§ËÒ (f∙g)(x), �f

g� (x) ¾ÃŒÍÁ·Ñé§ËÒ

â´àÁ¹


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áºº½ƒ¡ËÑ́ 6 1. ¡íÒË¹´ f={(1,3),(2,5),(3,7),(4,9)}, g={(3,16),(5,11),(7,12),(10,15)}

¨§ËÒ gof , fog


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2. ¡íÒË¹´ f(x)=4x+3, g(x)=3x-2 ¨§ËÒ (gof)(x), (fog)(x), (fof)(x),

(gog-1)(x), (g0f))-3), (fog)(2), (fofof-1)(2)


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3. ¡íÒË¹´ f(x)= �3x-2 , x≥02x-2 , x<0

, g�x-1�=3x-4

¨§ËÒ (gof)(x), (fog)(x), (gof )(2), (gof)(4), �f-1og�(x),

(g-1of)(x), (f-1og)(0), (g-10f)(5)


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4. ËÒ g(x) àÁ×èÍ f(x)=2x+4 ,g�f(x)�=5x+3


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5. ËÒ g(x)àÁ×èÍ f(x)=x-2 , g�f(x)�=x2-2x-3

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