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Let f(x)=x^(3)+x+1 and let g(x) be its i...

Let `f(x)=x^(3)+x+1` and let g(x) be its inverse function then equation of the tangent to `y=g(x)` at x = 3 is

A

`x-4y+1=0`

B

`x+4y-1=0`

C

`4x-y+1=0`

D

`4x+y-1=0`

Text Solution

Verified by Experts

The correct Answer is:
A
Let `(3,alpha)` be the point on `y=g(x) rArr (alpha, 3)` lines on `y=f(x) rArr alpha=1`
`"Also "x=f(g(x))`
`rArr" "g'(3)=(1)/(f'(g(3)))=(1)/(f'(1))=(1)/(4)`
`therefore" Tangent is y"-1=(1)/(4)(x-3)or x-4y+1=0`.
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