(x2 + 8)2
36x2 = (x2 + 8 + 6x)(x2 + 8
x3
7x = x(x2
p
6x2
2x + 15
6x
7) = x(x
6x) = (x + 2)(x + 4)(x
4)
7)(x + 1)
6 = x ) 2x + 15 = (x + 6)2 , x2 + 10x + 21 = 0 , (x + 7)(x + 3) = 0
x=
|x2 + 3x
2)(x
3
2| = 2
x2 + 3x
4 = (x + 4)(x
1) = 0
x2 + 3x = x(x + 3) = 0
(2n + 1) + (2n + 3) = 164 , 4n + 4 = 164 , n = 40
x=
4, 3, 0, 1
h(x) = 1/x
h(x+c) h(x)
c
h(1/x) = x h(2x) = 1/(2x)
h(1/x) h(2x)
=
1
x+c
1
x
c
f (x) = x2
(x+h)2 x2
h
f
=
2xh+h2
h
= 2x + h
16 F ( 2) =
[x, x + h]
f (x)
h 6= 0
F ( 4) F ( 2) F ( 1) F (0)
F ( 4) =
h(x+c) h(x)
c
4 F ( 1) = 2 F (0) = 3
T
F (2)
F (2) = 5
8
2
>
si x <
< x
F (x) = 2
si x =
>
:
3 + x si x >
s T
1
1
1
s
T =3
s=7
3 = 49k
T =
g(f ( 1))
f (x) = 3x2 12
f (f (2))
g(g(2))
f (g(2)) = f (5) = 75
f (x) = 2x + 5
f (1) = 7 f
1
3 2
s
49
(7) = 1
g(x) = 7
g(f ( 1)) = g( 9) = 16
f (1)
f
1
(7)
x
f (f (2)) = f (0) =
f (g(2))
12
g(g(2)) = g(5) = 2
f (x) =
p
3
x
f
p
3
x+1
1
p
3
f
x
x
f (x)
f ( x2 + 2)
f ( x+2
)
2
s
s=
s=
16t2 + 80t + 5 =
16(t
16t2 + 80t + 5
t
5/2)2 + 105
$1, 500(1 + 0.0425/2)20 = $2, 284.19
f (x) = ln((x + 2)(x
x=
2
x=3
4e2x
4e2x
2ex
12 = (2ex
( 1, 2) [ (3, 1)
( 1, 1)
2ex = 12
4)(2ex + 3) = 0 , ex = 2 , x = ln(2) ⇡ 0.693147
3))
y = 3 + 2(x + 1)3
g(x) = x4
g(x) = x4
7x2 + 12 = (x2
3)(x2
2,
4) = (x
p
3)(x +
p
3)(x
7x2 + 12
2)(x + 2)
p p
3, 3, 2
g(x) = x3 + 7x2 + 13x + 3
g(x) = x3 + 7x2 + 13x + 3 = (x + 3)(x2 + 4x + 1)
x=
p
4± 12
2
=
2±
p
3
P (x) = 8x3 + 5x2
x=
±1, ±3, ± 12 , ± 32 , ± 14 , ± 34
3
8
a + bi
i(4+i)
3 2i
=
1+4i 3+2i
3 2i 3+2i
=
11+10i
13
=
11
13
+
2
(x + 1)(x + 2)(x
P (x) = x4 +x3
x2 +x 2
i
P (x) = (x2 + 1)(x2 + x
i
1)
i(4+i)
3 2i
10
i
13
P
i
11x + 3
x = i, i, 2, 1
2) =