文档介绍：Section
1
: If f(x)= , then:
x
1 1
(a) f(−a)= = −;
−a a
1
(b) f(a−1)= = a;
a−1
√ 1 1
(c) f ( a )=√= = a−1/2;
a a1/2
1
(d) f(a2)= = a−2.
a2
: If f(x)=x2 + 5, then:
(a) f(−a)=(−a)2 +5=a2 +5;
1 1+5a2
(b) f(a−1)=(a−1)2 +5=a−2 +5= +5= ;
a2 a2
√√
(c) f ( a )=( a )2 +5=a +5;
(d) f(a2)=(a2)2 +5=a4 +5.
1
: If f(x)= , then:
x2 +5
1 1
(a) f(−a)= = ;
(−a)2 +5 a2 +5
1 1 1 · a2 a2
(b) f(a−1)= = = = ;
(a−1)2 +5 a−2 +5 a−2 · a2 +5· a2 1+5a2
√ 1 1
(c) f ( a )= √= ;
( a )2 +5 a +5
1 1
(d) f(a2)= = .
(a2)2 +5 a4 +5
√
: If f(x)= 1+x2 + x4, then:
√
(a) f(−a)= 1+(−a)2 +(−a)4 = 1+a2 + a4;
√(a4) · (1 + a−2 + a−4)
(b) f(a−1)= 1+(a−1)2 +(a−1)4 = 1+a−2 + a−4 =
a4
√√
a4 + a2 +1 a4 + a2 +1 a4 + a2 +1
= = √= ;
a4 a4 a2
√√√√
(c) f ( a )= 1+( a )2 +( a )4 = 1+a + a2;
√
(d) f(a2)= 1+(a2)2 +(a4)2 = 1+a4 + a8.
1
: If g(x)=3x + 4 and g(a) = 5, then 3a +4=5,so3a = 1; therefore a = 3 .
1
: If g(x)= and g(a) = 5, then:
2x − 1
1
1
=5;
2a − 1
1=5· (2a − 1);
1=10a − 5;
10a =6;
3
a = .
5
√
: If g(x)= x2 + 16 and g(a) = 5, then:
a2 +16=5;
a2 + 16 = 25;
a2 =9;
a =3ora = −3.
: If g(x)=x3 − 3 and g(a) = 5, then a3 − 3=5,soa3 = 8. Hence a =2.
√
: If g(x)= 3 x +25=(x + 25)1/3 and g(a) = 5, then
(a + 25)1/3 =5;
a +25=53 = 125;
a = 100.
: If g(x)=2x2 − x + 4 and g(a) = 5, then:
2a2 − a +4=5;
2a2 − a − 1=0;
(2a + 1)(a − 1) = 0;
2a +1=0ora − 1=0;
1
a = − or a =1.
2
: If f(x)=3x − 2, then
f(a + h) − f(a) = [3(a + h) − 2] −[3a − 2]
=3a +3h − 2 − 3a +2=3h.
: If f(x)=1− 2x, then
2
f(a + h) − f(a)=[1− 2(a + h)] −[1 − 2a]=1− 2a − 2h − 1+2a = −2h.
: If f(x)=x2, then
f(a + h) − f(a)=(a + h)2 − a2
= a2 +2ah + h2 − a2 =2ah + h2 = h · (2a + h).
: If f(x)=x2 +2x, then
f(a + h) − f(a)=[(a +