8. If 3 f(x) - 2f (1/x)=x,then f(2) is
Answers
Answer:
Differentiate 3f(x)−2f(
x
1
)=x with respect to x,
3f
′
(x)−2f
′
(
x
1
)(−
x
2
1
)=1
3f
′
(x)+
x
2
2
f
′
(
x
1
)=1 (1)
Put x=2 in equation (1),
3f
′
(2)+
2
2
2
f
′
(
2
1
)=1
3f
′
(2)+
2
1
f
′
(
2
1
)=1 (2)
Put x=
2
1
in equation (1),
3f
′
(
2
1
)+
(
2
1
)
2
2
f
′
⎝
⎜
⎜
⎛
2
1
1
⎠
⎟
⎟
⎞
=1
3f
′
(
2
1
)+
4
1
2
f
′
(2)=1
3f
′
(
2
1
)+8f
′
(2)=1
3f
′
(
2
1
)=1−8f
′
(2)
f
′
(
2
1
)=
3
1
−
3
8
f
′
(2)
Substitute above value in equation (2),
3f
′
(2)+
2
1
(
3
1
−
3
8
f
′
(2))=1
3f
′
(2)+
6
1
−
3
4
f
′
(2)=1
3f
′
(2)−
3
4
f
′
(2)=1−
6
1
3
9f
′
(2)−4f
′
(2)
=
6
6−1
5f
′
(2)=
2
5
f
′
(2)=
2
1
Therefore, the value of f
′
(2) is
2
1
.
Step-by-step explanation:
Answer:
we have to put only the value of x =2 . then we will get answer. answer is 5.
