Discuss the differentiability of `f(x) =[x]+ sqrt({x})),` where [.] and {.} denote the greatest integer function and fractional part repectively .

Options

A. `[x] +sqrt({x})`
B. `[x] + {x}^(2)`
C. `[x]^(2)+{x}`
D. `{x}+sqrt({x})`

Answer

B

Explanation

`y=[x]+sqrt({x})`
` implies [y] +{y} =[x]+sqrt({x})`
`implies {y}=sqrt({x}) … " " ( :' [y]=[x])`
`implies {x}+[x]=[y]+{y}^(2)`
`implies x=[y]+{y}^(2)`
`implies f^(-1)(x)=[x]+{x}^(2)`