4
)µ
(1) ¼ê½Â••X = (−∞, 0)
S
(0, ∞)§f(−1) = 0, f (1) = 0, f(2) = −
3
2
(2) ¼ê½Â••X = [−|a|, |a|]§f(0) = |a|, f(a) = 0, f
−
a
2
=
√
3
2
|a|
(3) ¼ê½Â••(−∞, 0)
S
(0, ∞)§s(1) =
1
e
, s(2) =
1
2e
2
(4) ¼ê½Â••
n
x
x ∈ R, x 6= kπ +
π
2
, k ∈ Z
o
§g(0) = 0, g
π
4
=
π
2
16
, g
−
π
4
= −
π
2
16
(5) ¼ê½Â••X = (−∞, ∞)§x
−
π
2
= −1, x(−π) = −1
(6) ¼ê½Â••X = (−∞, −2)
S
(−2, 1)
S
(1, +∞)§f(0) = −
1
2
, f(−1) = −
1
2
5. ¦e¼ê½Â•9Š•µ
(1) y =
√
2 + x − x
2
(2) y =
√
cos x
(3) y = ln
sin
π
x
(4) y =
1
sin πx
)µ
(1) ¼ê½Â••X = [−1, 2]§Š••
0,
3
2
(2) ¼ê½Â••
h
2kπ −
π
2
, 2kπ +
π
2
i
(k ∈ Z)§Š••[0, 1]
(3) ¼ê½Â••
1
2k + 1
,
1
2k
(k ∈ Z)§Š••(−∞, 0]
(4) ¼ê½Â••(n − 1, n)(n = 0, ±1, ±2, ···)§Š••(−∞, −1]
S
[1, +∞)
6. f(x) = x + 1, ϕ(x) = x − 2§Á)•§|f (x) + ϕ(x)| = |f(x) + |ϕ(x)|
)µd®•§f(x)ϕ(x) > 0=(x + 1)(x − 2) > 0§Kx > 2½x 6 −1.
7. f(x) = (|x| + x)(1 − x)§¦÷veˆªxŠµ
(1) f(0) = 0
(2) f(x) < 0
)µ
(1) ‡f(x) = 0§K|x| + x = 0½1 − x = 0§=x 6 0½x = 1
(2) Ï|x| + x > 0§K‡f(x) < 0§•‡1 − x < 0=Œ§=x > 1
8. ã1-5L«>³|V ! ½>{R
0
ÚŒC>{R|¤>´.3˜ãØ•žmS§A, Bü:m>ØV Œ±w
¤˜‡~þ.¦Ñ>6IÚŒC>{R¼êª.
)µd®•9ÔnÆ•£§V = I(R
0
+ R).
9. 3˜‡Î/NìS?,«M—§TÎ/Nì .Œ»´a§p•h§?M—pÝ´x£ã1-6¤. T
M—NÈV Úxƒm¼ê'XV = V (x)§¿Ñ§½Â•ÚŠ•.
)µd®•§V = πa
2
x§§½Â••[0, h]§Š••[1, πa
2
h]
10. ,/Y± ¡È´˜‡F/§Xã1-7§.°2’§>–•45
o
§CDL«Y¡§¦¡ABCD¡
ÈS†Yh¼ê'X.
)µd®•9ã§S = h(h + 2).
11. k˜•H¶³§X^Œ»•Ròűz¦¨ωlÝ„Ýl¶³SåL-Ô§¦-Ô.¡†/¡
ålsÚžmt¼ê'X£ã1-8¤.
)µd®•9ã§s = H − ωRt
t ∈
0,
H
ωt
12. y = f(x) =
1 + x
2
, x < 0
x − 1, x > 0
§¦f(−2), f(−1), f (0), f(1)Úf
1
2
.
)µd®•§f(−2) = 5, f (−1) = 2, f(0) = −1, f(1) = 0, f
1
2
= −
1
2
.
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