Question

If `f(x)=(sin([x]pi))/(x^2+x+1)` , where `[dot]` denotes the greatest integer function, then `fi son eon e` `fi snoton e-on ea n dnon-con s t a n t` `fi sacon s t a n tfu n c t ion` `non eoft h e s e`
A. `f` is one-one
B. `f` is not one-one and non-constant
C. `f` is a constant function
D. None of these

Answer 1

Correct Answer - C
`f(x)=(sin[x]pi)/(x^(2)+x+1)`
Let `[x]=n ~= "integer" `
` :. sin[x] pi=0`
or `f(x)=0`
Hence, `f(x)` is constant function.