1-*

1-*

1-*

|x - a| x< a - x > a +

x 1-*

1-*

1-*

3( i ) f (x) = ( i )D( f ) = R - {1} (ii) f (x) = (ii)D( f ) = {x | x2(x + 2)(x - 2) 0} = {x | x - 2 x 2 x = 0} (iii) f (x) =

(iii)D( f ) = {x | (x + 5)(x - 4) > 0}{x| (x + 6)(x - 2) > 0}

= {x | x < - 5 x > 4}{ x < - 6 x > 2} = {x| < - 6 x > 4} 21-*

1-*

1-*

6( i ) f (x) = x3 - 1R R

(ii) g(x) = x4 RR

(ii)(i) (ii) 1-*

1-*

(a) f (b)(c)

1-*

1-*

1-*

1-*

ad bcac0f (x) = R - { - }R - { }f - 1(x)

f - 1(x) = 1.2-1

1-*

1-*

1-*

f[a, b][a, b]x1x2x1 < x2f (x1) f (x2)f (x1) < f (x2)f (x)[a, b]x1 < x2f (x1) f (x2)f (x1) > f (x2)f (x)[a, b]

monotonic function 1.3-21-*

1-*

f (x) = - x2 (0, )

3

x1(0, )x2(0, )x1 < x2 f (x1) - f (x2) = - x - (- x ) = x - x = (x2 - x1)(x2 + x1) > 0 x1 < x2f (x1) > f (x2)f (x) x2 - x1 > 0x1 + x2 > 0

1-*

(1)f (-x) = f (x)f (x)y(x = 0)even function(2)f (-x) = - f (x)f (x)(0, 0)odd function y = f (x)[ - l, ]>0x[ - , ]

1.3-3 1-*

f (x)y(x = 0)yf (x)(0, 0)

1-*

1-*

1-*

1-*

1.4-1

(1)constant functionf (x) = c cR(2)power functionf (x) = xa aR(3)exponential functionf (x) = ax a>0a1(4)logarithmic functionf (x) = logax a>0a1(5)trigonometric functionf (x) = sinx f (x) = cosxf (x) = secxf (x) = cscx(6)inverse trigonometric functionf (x) = Arcsinx f (x) = Arcsecxf (x) = Arccscx

1-*

1-*

1-*

absolute functionf (x)

nN

f (x)f (x) = | x | 1-*

1-*

1-*

1-*

1-*

1-*