Let `f(x)=(sqrt(x-2sqrt(x-1)))/(sqrt(x-1)-1)xdot` Then `f^(prime)(10=1` `f^(prime)(3/2)=-1` `dom a inoff(x)i sxgeq1` range of `f(x)i s(-2-1)uu(2,oo)`

Options

A. `f(10)=1`
B. `f'(3//2)=-1`
C. domain of `f(x) is x ge 1`
D. range of `f(x) is (-2, -1)] cup (2,00)`

Explanation

`f(x)(sqrt((x-1)^(2))+1-2sqrt(x-1))/(sqrt(x-1)-1)`
`=(|sqrt(x-1)-1|)/(sqrt(x-1)-1)x`
`={{:(-x",", if x in [1,2)),(x",", if x in (2,oo)):}`