The least integral value of
`f(x)=((x-1)^(7)+3(x-1)^(6)+(x-1)^(5)+1)/(x-1)^(5)`, `AAx gt 1` is

Options

A. `8`
B. `6`
C. `12`
D. `18`

Answer

B

Explanation

`(b)` `f(x)=(x-1)^(2)+3(x-1)+1+(x-1)^(-5)`
Consider `x-1=a gt 0` (as `x gt 1`)
`:.` We have `a^(2)+3a+1+a^(-5)`
Consider quantities `a^(2),a,a,a,1,a^(-5)`
Using `A.M. ge G.M.` , we have
`(a^(2)+a+a+a+1+a^(-5))/(6) ge 1`
`impliesa^(2)+3a+1+a^(-5) ge 6`
`impliesf(x) ge 6 AA x gt 1`