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Find the domain and range of f(x)="sin"...

Find the domain and range of `f(x)="sin"^(-1)(x-[x]),` where [.] represents the greatest integer function.

Text Solution

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The correct Answer is:
`(-1, 0) cuop ( 0, 1) `
`f (x) = sin^(-1)x , g (x) = =[x]`
f(x) is continuous for all ` x in [ -1,1]` and g(x) is continuous for all ` x in R - I `
Therefore , domain of continuity of (f -g) (x) = ` sin^(-1) x - [x]` is
`[-1,1] cap R -I = (-1,0) cup (0,1)`
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