Let `g(x)={(2e, "if", xle1),(log(x-1),"if",xgt1):}` The equation of the normal to `y=g(x)` at the point `(3,log2)`, is

Options

A. `y-2x=6+log2`
B. `y+2x=6+log2`
C. `y-2x=6-log2`
D. `y+2x=-6+log2`

Answer

B

Explanation

For the point `(3,log2)`, we take `y=g(x)=log(x-1)`, then `(dy)/(dx)=1/((x-1))`
At `(3,log 2),((dy)/(dx))_((3,log2))=1/2`
Slope of normal `=(-1)/(1//2)=-2`
`:.` Equation of normal is
`y-log2=-2(x-3)`
`implies h+2x=6+log2`