Question

The domain of the function `f(x)=1/(sqrt({sinx}+{sin(pi+x)}))` where `{dot}` denotes the fractional part, is `[0,pi]` (b) `(2n+1)pi/2, n in Z` `(0,pi)` (d) none of these

Answer 1

`f(x)=(1)/(sqrt({sinx}+{sin(pi+x)}))=(1)/(sqrt({sinx}+{-sinx}))`
Now, `{sinx} +{-sinx}={(0",",sinx " is an integer"),(1",", sinx " is not an integer"):}`
For f(x) to get defined,
`{sinx} +{-sin} ne 0`
or ` sinx ne ` integer
or `sinx ne +-1,0`
or ` x ne (n pi)/(2), n in I`