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if x=(1+t)/t^3 ,y=3/(2t^2)+2/t satisfies...

if `x=(1+t)/t^3 ,y=3/(2t^2)+2/t` satisfies `f(x)*{(dy)/(dx)}^3=1+(dy)/(dx)` then `f(x)` is:

A

`x`

B

`(x^(2))/(1+X^(2))`

C

`x+x+(1)/(x)`

D

`x-(1)/(x)`

Text Solution

Verified by Experts

The correct Answer is:
A
`(dy)/(dx)=(dy//dt)/(dx//dt)=(-((3+2r))/(t^(3)))/(-((3+2t))/(t^(4)))=t`
Since `f(x)((dy)/(dx))^(3)=1+(dy)/(dx)`
`rArr" "f(x)t^(3)=1+t`
`rArr" "f(x)=(1+t)/(t^(3))=x`
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