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1

1

.


1

1.1


1

f

(x, y ) (x,z) f y = z

f (x,y) f

y f x

x (independent variable)

y (dependent variable)


1

1

2


1

1

  • r

  • r

  • r

  • r


1

2

  • y()

  • 1

  • y

  • 1


1

r1 = {(3,4),(5,6),(7,8)} r2 = {(3,4),(3,5),(7,8)}

r1, r2

1)

2)


1

1)

r1 = {(3,4),(5,6),(7,8)}

r2 = {(3,4),(3,6),(7,8)}

r2


1

2)

r1 = {(3,4),(5,6),(7,8)}


1

r2 = {(3,4),(3,6),(7,8)}

r2


1

f

f

f

f X Y f X f Y

f X Y


1

Y

X

f

f(x1)

f(x2)

f(x3)

x1

x2

x3

f (one to one function) x1, x2 X f(x1)= f(x2) x1 = x2


1

f f f-1


1


1

1. (polynomial functions)

2. (rational functions)


1

1. (polynomial functions)

n

f n


1

2. (rational functions)

f(x)

P(x) Q(x) Q(x) 0


1

(transcendental functions)

1.

2.

3.

sin, cos, tan, sec, cosec cot


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1.2


1

f(x) x=a L f a L


1

x= 0, 1, 2, 3, 4


1

f x = a

1.f(a)

2.

3.


1

x= 1, 2, 3

f x = 1

f(1) = 1

f x = 2 f(2) = 2

f x = 3 f(3) = 2


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1.3


1

(imaginary number)

a+bi


1

(complex number) z

(a,b)

z = a + bi

a z

b z


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1.

z1 = a + bi z2 = c + di

z1 = z2 a = c b = d

2.

z1 = a + bi z2 = c + di

z1 + z2 = (a+c) + (b+d)i

3.

z = a + bi k

kz = ka + kbi


1

4.

z1 = a + bi z2 = c + di

z1 z2 = (a + bi)( c + di) = (ac-bd)+(ad+bc)i

5.

z1 = a + bi z2 = c + di


1

6. a + bi

z = a + bi z

7. (conjugate) z


1


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